Degree of the Polynomial Is the Highest Exponent from All Terms
Standard form is writing the polynomial from the highest exponent to the lowest exponent.
Degree of the polynomial is the highest exponent from all terms
a) Write each polynomial in standard form: b) Give the degree of each polynomial
1. x + x2 / 2. 3n2 + 6 - 5n / 3. 8 - 2x3 + 4x24. 2 + x2 + 4x / 5. 6 + 7x / 6. 7 - 8a2 + 6a3
7. y3 - 4y + 6 - y2 / 8. x2 + 4 - x / 9. x2 = x4
10. 3m - 7m3 + 3 / 11. 5a + 7a4 - 6a2 / 12. 6x3 + x + x2
13. 6 + x2 - 4x / 14. x3 - 8 + 6x / 15. y2 - 7y - 3y3
16. x - 6x2 + 9 / 17. 6x + 8x3 - 2x2 / 18. 12x2 - 6x3 + 7 + x
Adding and Subtracting Polynomials
Add only like terms which have the same letter and exponent
Rewrite all like terms under each other
Change all the signs in parentheses after a subtraction sign only
Simplify:
1. 2y + (4y - 3) / 2. 3k + (2k + 4) / 3. 9m + (-2m - 7)4. (2x2 - 1) + (3x2 + 7) / 5. (5a2 + 3) + (-7a2 - 4) / 6. (2y - 3) + (4y + 5)
7. (2x2 - 3x + 5) + (4x2 + 6x - 8) / 8. (a2 - 2a + 1) +(a2 - 4) / 9. (3x) - (2x)
10. 2k - (2k + 4) / 11. 6x - (2x + 7) / 12. (7x - 5) - (5x + 3)
13. (10 - 2k) - (7 - 3k) / 14. (z2 – 3z + 10) – (z2 + 5z – 6)
15. (8p2 + 5) – (3p3 - 3p2 + 2p – 9) / 16. (2a2 – 3a + 5) – (a2 -2a – 4)
17. (11m3 + 3m2 - m) - (-6m3 + 3m2 + 4m) / 18. (3d3 - 10d2 + d + 1) + (5d3 + 2d2 - 3d – 6)
19. Find the perimeter of triangle ABC.
/ 20. Find the perimeter of quadrilateral ABCD.
21. Find the sum of the perimeters of triangle ABC and Quadrilateral ABCD. / 22. Subtract the perimeter of Triangle ABC from the perimeter of quadrilateral ABCD.
Find each sum or difference and write your answer in standard form:
1. (3x2 - 4) + (5x2 + 8) / 2. (5x3 + 6x2) + (x3 - 12x)3. (5x2 + 4x + 8) - (3x2 + x + 3) / 4. (8x2 - 4x + 1) - (3x2 + 6x - 4)
5. (4y2 - 3y + 8) + (6y2 + 6y - 9) / 6. (a3 + 8a2 + 6a) + (8a3 + 2a2 - 6a)
7. (7y3 + 2y - 7) - (2y3 + y + 3) / 8. (n3 + n2 + n) - (2n3 + 3n2 - 2n)
9. (7y2 + 8y + 1) + (y2 - 5y - 3) / 10. (9x2 + 3x + 4) + (2x2 - 9x - 5)
11. (3a + 4a3 - 8) + (a2 + 2a - 7) / 12. (2x3 + 6x - 7) + (3x2 - 9x - 5)
13. (x3 + 3x2 - 4x) - (2x2 + 3x + 1) / 14. (4x2 - 7x + 8) - (2x3 + 8x - 5)
15. (3c2 + 4c - 6) - (3c + 8) / 16. (2y3 - 7y + 10) - (y3 + 6y - 7)
17. (3x - 7x2 - 3) + (x2 + 5x) / 18. (3y3 + 8y2 - 3) + (2y - 5y2)
19. 5a2 + 7a - 11) + (a + 4 - 5x2) / 20. (6 - 8x) + (7x3 + 2x + 15)
21. (2x - 10x2 + 7) - (x2 + 8) / 22. (3x3 - 10x + 8) - (2x2 + 7x + 8)
23. (x2 - 3 + 7x) - (-2x3 + 3x2 - 7x) / 24. (6x3 - 9 + 8x) - (2x2 + 6x - 11)
25. (9 - 5x3 - 6x2) + (x + 6x2 - 4) / 26, (x + 3x2 - 4x3 + 6) - (x3 + 3x2 - x)
Multiplication
1st Multiply the coefficients
2nd Add the exponents of the different letters
Simplify each expression:
1. a ∙ a ∙ a / 2. y2 ∙ y ∙ y3 ∙ y / 3. 2c2 ∙ c / 4. b2 ∙ b35. r3 r5 / 6. (-t2)(-t6) / 7. (-x3)(-x3) / 8. (2x)(3x2)
9. (3ab)(5a2b) / 10. r2(3rs5) / 11. (-2pq)(-p2q) / 12. (-2xz)(4x2y)
13. x(xy)(x2y) / 14. (2r)(3st)(rst) / 15. 2x3(-3xy2)(-x3y4) / 16. wz2(-w3yz)(yz2)
17. x ∙ xn / 18. yn ∙ yn / 19. a2 ∙ an - 2 / 20. t2n ∙ tn
Multiply:
1. (2a)(3b) / 2. (-4m)(-3n) / 3. (6k)(-2m) / 4. (3x)(-3z)(2)5) (-2k)(-3p) / 6. (-6a)(b) / 7. (2c)(3.5d) / 8. (-3p)((-4.1r)
9. (2a)2 / 10. (3m3)2 / 11. (7y)(y4)2 / 12. (5b3)(-2b)
13. (4p4)(-6p)2 / 14. (-3a2)(-2a3) / 15. (5k4)(-3k2) / 16. (2p)2(-4p3)
17. 4x2)3 / 18. (2y4)2 / 19. (-2d2)3 / 20. (-3x2)2
21. (2a2b3)(6ab2) / 22. (-3x3y3)(-4xy2) / 23. (p3r3)(9p2r) / 24. (2c)2(3b3)
25. (2a2)2 / 26. 2(a2)3 / 27. (-3x2)3 / 28. (2p2r3)(5pr2)2
29. (-4b4)3 / 30. 3(-3x2y)(xy6) / 31. (a2b3)(12x3y) / 32. ( -6xy3)2
Simplify:
1. 2x(x + 3x2) / 2. -4(-y + 2y2) / 3. 2a(3a + 1)` / 5. 2(a2 + 5a - 1) / 6. -2m(m3 - 3m - 4)
7. -3(f2 - 2f - 8) / 8. 4p(p2 - 3p - 2) / 9. –r(r3 - 9r + 6)
10. a(4 - a -5a2) / 11. 2x(2x3 - 4x + 3) / 12. 4a2(-a2 - 3a + 9)
13. 4x + 2(x + 1) / 14. 4(a - 3) - 3a / 15. -2p - 2(p - 3) + 6
16. 4(2a - b) - 3(a + b) / 17, 4(m - 1) + 3(m + 5) / 18. 4a(2b - a) - 3a(2b + a)
19. 4xy(4x2y - 3xy2 + 7y2) / 20. -2rs(r3 - 3r2s + 5s2) / 21. 3(x - y) - 2(x - y)
22. 2x(x - 3) + 5(x2 - 2x) / 23. 7(2x - y) - 2(x - 3y) / 24. 2a2b(3ab - 7a2b2)
Division
1st Divide the coefficients
2nd Subtract the exponents of the different letters (cancel common factors)
`
Divide:
1. -6xy2y / 2. abc
-ac / 3. 8cd
-4cd / 4. 12wz
3z
5. 24z6
6z2 / 6. 27x7y
3x2 / 7. -18x6
-9x3 / 8. -21a6b8
-3ab3
9. 4x + 8
2 / 10. 6y - 12
3 / 11. -14b + 21
7 / 12, 3y4 + 6y3 + 12y2
3y
13. 20cd
4d / 14. 18gh
2g / 15. 40ry
10r / 16. -12ab
2a
17, -12pq
-3q / 18, -15st2
5st / 19. y3y2
y2x2 / 20. 12c2d3
-2cd2
21. 2a + 12
2 / 22. 18y + 6
-6 / 23. 9a - 18b
9 / 24. -25xy2 - 15xy2
-5xy
25. 4x5 - 8x3 + 12x2
4x2 / 26. 32c - 16b + 4a
4 / 27. 6x3 - 9x2 - 3x
3x
28. 28x2y2 - 21xy2 + 14xy
7xy / 29. 9a2b2c2 - 15abc2
3abc / 30. 35c3d2e + 50c4d3e2
5cde
31. 25u2 - 15u - 5
-5 / 32. 9 - 6t - 3t3
3 / 33. 8a3 - 4a2 + 2a
2a
34. 12x2 - 9x3 + 6x4
3x / 35. x3y - 2x2y2 + xy2
xy / 36. 2u3v + 4u2v2 + 6uv3
2uv
37. 8z2xy - 12x2zy + 16zx2y3 - 24z2x3y3
4zxy / 38. 56a4b4c3 - 49a3b3c2 + 35ab2c2 - 28a2bc4
-7abc
Simplify:
1. 7(2x2)(4y2) / 2. 2(2x - 5) + 3 - 2x / 3. 12 - 3(2x + 5)4. (-4x2y)2 / 4. (2x3y2)(-3xy)(5x5y2) / 6. -12x2y3
2xy
7. 2xy2(7x - 6y + 8) / 8. 3(x + 2y) - 4(2x + y) / 9. (3z2y)3
10. (m4n5) (2m2n2) / 11. 25x2 + 15x - 5
5 / 12. -2x(5x2y)(2x3)2
13. 12x - 4(2x + 3) / 14. (5x - 6y) - (8x + 7x) / 15. (5x - 6y) + (8x + 7x)
16. 2(x + 7) + 2(3 - 4x) / 17. -5x2(2x2 + 8x - 6) / 18. 25a - 15b + 5c
5
19. 5a2b(2ab2 - 3b) / 20. 2(4x + 7) - 13 / 21. -3(x - 5) + 2(3x - 7)
22. (6y2 - 5y + 8) + (y2 + 6y - 10) / 23. (a3 + 7a2 - 6a) + (8a3 + 5a2 - 3a)
24. (5y3 + 3y - 7) - (4y3 + 2y + 3) / 25. (3n3 + n2 + n) - (2n3 + 3n2 - 9n)
26. 3x - 6 + 9 + 2x / 27. 4x2 - 3x + 2x2 - 7x / 28. 7 - (4x + 7)
29. 4(x - 5) + 3(3 - 4x) / 30. 25x3 + 20x2 + 15x2
5x2 / 31. (2x)2(-3y)3
Simplify:
1. From 4x + 2y subtract x - 4y / 2. Subtract 5a - 7b from 3a - 9b3. From 5x2 + 5x - 4 subtract x2 - 3x + 5 / 4. Subtract 7r2 + 3r - 8 from 10r2 - 3r - 7
5. From m2 + 5m - 7 subtract m2 - 3m -4 / 6. From 12x - 6y + 9z subtract -x - 3z + 6y
7. Subtract 2x2 - 3x + 7 from x2 + 6x - 12 / 8. Subtract 5x + 4y - 6z from 3x - y - 8z
9. 5(d + 3) - 10 / 10. 3(2 - 3c) + 5c / 11. 7 + 2(7x - 5)
12. -2(x - 1) + 6 / 13. -4(3 - 6a) - 7a / 14, 5 - 4(3c - 5)
15. 8 + (4x - 6) / 16. 9 - (5t + 6) / 17. 5x(2x - 3) + 9x
18. (6b + 4) - 2 / 19. –(6x - 7) + 14 / 20. 4 - (2 - 8a)
21. 12y - 3y(2y - 4) / 22. 7x + 3(2x - 1) - 8 / 23. 7c - 4d - 2(4c - 3d)
24. 3a - 2a(5a - 1) + 5a2 / 25. 4(2x + 5) - 3(2 - 7x) / 26. (3y - 6) - (8 - 9y)
27. (4a - 3b) - (5a - 2b) / 28. (2c + 3d) + (-6d - 2c) / 29. (a - 2b) + (2a + 5b)
Multiplying Polynomials - Stapling
1st Draw your 2 staples and multiply
2nd Draw a line and add your two new terms
3rd Multipy the first terms
4th Multiply the last terms
Multiply:
1. (x + 3)(2x - 5) / 2. (3w + 4)(2w - 1) / 3. (x + 4)(x + 3)4. (a - 11)(a + 5) / 5. (3x - 4)(x - 5) / 6. (4x + 3)(x - 7)
7. (5x - 3)(4x + 2) / 8. (3y + 7)(4y + 5) / 9. (3x + 7)(x + 5)
10. (5x - 2)(x + 3) / 11. (a - 6)(a + 8) / 12. (2x + 1)(3x - 1)
13. (k + 4)(3k - 4) / 14. (y - 4)(2y + 3) / 15. (x + 7)(x + 5)
16. (2x + 1)(4x + 3) / 17. (6x - 5)(3x + 1) / 18. (n - 7)(n + 4)
19. (5n - 1)(n + 4) / 20. (y + 9)(y - 11) / 21. (4x - 7)(2x - 3)
22. (x2 + x - 1)(x + 1) / 23. (x + 6)(2x2 - 6x - 8)
24. (3m2 - 7m + 8)(m - 2) / 25. (x + 2)(2x2 - 3x + 2)
26. (a2 + a + 1)(a - 1) / 27. (x - 2)(x2 + 4x + 4)
28. (2n - 3)(n2 - 2n + 5) / 29. (3x + 1)(4x2 - 2x + 1)
30. (2x2 - 5x + 2)(4x - 3) / 31. (2x2 - 9x + 11)(2x + 1)
32. (x - 5)(x2 + 5x - 3) / 33. (2x2 + 5x - 4)(2x + 7)
34. (2x - 1)(x2 - 7x + 1) / 35. (x - 5)(x2+ 2x + 5)
36. (x + 9)(x + 7) / 37. (3y - 7)(2y + 1) / 38. (x + 7)(x - 7)
39. (2x - 5)(2x + 5) / 40. (3x + 5)2 / 41. (x - 10)2
42. (2x + 3)(x + 7) / 43. (x + 12)(x - 12) / 44. (5x + 1)(5x - 1)
Simplify:
1. m2 + m - 6 + 3m -2 / 2. 5s + 2 - 5s - 7 + 4s3. t4 + 3t3 - 2t4 + 3 + 2t3 - 1 / 4. 6x2 + 8x - 8 - 2x2 - 9x + 4
5. -3 + 16z2 - 8z3 + 5z2 + 11 + 4z / 6. -7a - 3a2 + 8a + 12a2 - 9
7. 5x3 + 3x - 4 - 3x2 + 8x3 + 6 - 6x / 8. 3y4 + 3y + 3y3 - y2 + y + y2
9. n2 + 3n + 4n2 + n3 - 3n3 + 2 / 10. 8r2 + 4r3 - 3r2 - r - 4r2
11. (4y3 - 2y2 + y) + (y3 - 2y2 + 44) / 12. (4m2 + m - 3) + (2m2 + 7)
13. (6n2 + 4n + 3) - (3n2 - 5n + 1) / 14. (5p3 + 2p2 - p + 4) - (2p3 - p2 + p - 1)
15. (4y2 + y - 5) + (3y2 - 5y + 6) / 16. (8x2 - 4x + 2) - (5x2 - 3X + 4)
17. (4m2 - 3m + 3) - (2m2 - 3m - 3) / 18. (5r3 - r2 - 5) + (-6r3 - r2 + 3)
19. x3
x / 20. 12x2y
3xy / 21. -6m3n2
-3mn / 22. 6x - 9y + 12
3
23. (2a2)(5ab) / 24. (5x2y3)2 / 25. (-4a2b)(7a5b3) / 26. (2x)2(-5xy2)
27. 15x2y + 10xy
5xy / 28. 3x2(2x - 7) / 29. -14x2y5
-7x2y2 / 30. 15x2 - 10x + 5
5
31. (-3ab)(4ab) / 32. (2x)3 / 33. 3x2y(5x - 6y) / 34. -15a2b2
-5ab
35. 9 - 3x + 15 - x / 36. 8x - 5y - x + 9 / 37. 5 - (2x - 8) / 38. 3(2x + 5) - 10
Zero Exponents - anything raised to the zero power is 1
Negative Exponents moves the term to the opposite location in a fraction with a positive exponent
Top becomes bottom
Bottom becomes top
Find the value
1. 70 / 2. 4 ∙ 50 / 3. (3 + 5)0 / 4. 5-25. (3 ∙ 4)-2 / 6. 3-2 / 7. 2-4 / 8. 10-1
9. 10-2 / 10. 70 + 6 / 11. 70 + 6-2 / 12. x0
13. (1 + 3)0 / 14. 10-3 / 15. 9-1 / 16. 90 + 40
17. -3 ∙ 50 / 18. 8-2 / 19. 50 + 3-2 / 20. 5-3
Simplify:
1. 8x-3 / 2. (2x)-4 / 3. -10c-3 / 4. (-2x)-35. 1
4x-3 / 6. 1
(4x)-2 / 7. 3
5x-3 / 8. 4
(3a)-3
9. a4b-3
c2d-4 / 10. x2y-4
z-3 / 11. 2a-2b5
3c3d-4 / 12. 3x-5
4y-2z-1
13. x-2x5 / 14. a3a-6 / 15. n-4n-2 / 16. y-3y0
17. x4
x-2 / 18. a-3
a2 / 19. 6n-2
8n-6 / 20. -2c-6
4c-4
21. 5a4b-5
10c2d-2 / 22. 9x-2y-4
3z3 / 23. 2a5b-8
3cd-4 / 24. 2x-3
4y-3z-1
25. 8x-5y4 / 26. y(2x)-4 / 27. -10c-2 / 28. (-2x)-2
Simplfy:
1. 6x + (5x - 8) / 2. 2x - (9x - 4) / 3. -9 - (12 - 3x)4. –(5x + 5) - 4x + 8x / 5. 7(2x - 4) - (10 - 3x) / 6. -6(5 + x) + (13x + 1)
7. –(12 - 4x) + 8(10 - x) / 8. 7(2x + 2) - 9(-1 + 6x)
9. 4(-3x - 5) - (10 + 4x) / 10. 6x + (14x - 5) + (17 - 3x)
11. –(2 - x) - 3(6 + 8x) - 12 / 12. (4x - 9) + 8(2x + 3) - 7x
13. 11 - (3x - 6) + 2(4x + 5) + x / 14. 2(x + 2) -5(x - 2) - 12x + 7
15. –(5y - 6) + 4(3 + 5y) / 16. (-9y + 5) - 8(-y - 2)
17. 2(7 + 6y) + 15(y - 1) / 18. 5(-3y - 1) - (6 - 5y) + 8
19. 4(3 + 7y) + 6(2 - y) / 20. 7x - 4(6 - x) + 12
Simplify:
1. (y + 5)(y + 7) / 2. (c - 3)(c - 7) / 3. (x + 4)(x - 8)4. (w + 3)(w - 9) / 5, (x + 5)2 / 6. (2x - 1)(x + 8)
7. (11y + 9)(12y - 6) / 8. (8x + 9y)(3x + 2y) / 9. (2r + 7)(3r + 5)
10. (7 - 5x)(7 + 5x) / 11. (2x - 3)2 / 12. (6a - 1)2
13. 15 - (7x - 6) + 5(4x + 7) + x / 14. -3(x + 2) + 6(x - 2) - 10x + 7
15. –(7y - 6) + 8(3 + 3y) / 16. (-5y + 7) - 4(-y - 2)
17. -7(7 + 2y) + 5(y - 5) / 18. 7(6y - 12) - (8 - 5y) - 23
19. (5y3 - 2y2 + y) - (y3 - 7y2 + 15) / 20. (4m2 + m - 3) - (2m2 + 13)
21. (4n2 + 5n + 9) + (3n2 - 6n + 1) / 22. (2p3 + 5p2 - p + 4) + (2p3 - p2 + p - 1)
23. (2y2 + y - 5) - (5y2 - 8y + 7) / 24. (8x2 - 4x + 2) + (2x2 - 7x + 14)
25. (4m2 - 3m + 3) + (6m2 - 2m - 1) / 26. (5r3 - r2 - 5) - (-6r3 - r2 + 3)
27. x7
x2 / 28. 12x5y
2xy / 29. -63m4n3
-3mn / 30. 10x - 5y + 15
5
31. (7a2)(5ab) / 32. (4x5y2)2 / 33. (-3a2b)(8a6b4) / 34. (-3x)2(-2xy5)
35. 12x2y + 16xy
4xy / 36. 4x2(x - 8) / 37. -28x2y4
-7xy2 / 38. 18x2 - 12x + 6
6
Scientific Notation
. x 10a
1st Have only one digit to the left of the decimal point all numbers are to the right and the rest of the digits go after the decimal point to the right
2nd The exponent represents the number of times you moved the decimal point
If a is negative the number is a small decimal
If a is positive the number is a big number
1. 23, 000,000,000 / 2. .0000000000067 / 3. 458,000,0004. 20,000,000 / 5. .00000098 / 6. 32,000,000,000,000
7. .00000000009 / 8. 210,000,000 / 9. .00000000054
10. 9,000,000 / 11. .0000000012 / 12. .00000000000034
13. 68,500,000 / 14. 4,800,000,000 / 15. .0000000041
16. .00000805 / 17. 7,650,000,000,000,000 / 18. .00000065
19. .000000000005 / 20. 7,800,000,000 / 21. .0000000091
22. 500,000,000 / 23. .0000098 / 24. 34,000,000,000
Write in standard form:
1. 2.3 x 106 / 2. 3.76 x 109 / 3. 3.5 x 10-64. 5.0 x 10-5 / 5. 4 x 10-4 / 6. 7.09 x 1012
7. 5.3 x 108 / 8. 2.16 x 107 / 9. 8.5 x 10-8
10 . 5.0 x 10-8 / 11. 7.9 x 10-6 / 12. 5.9 x 1010
13 . 1.35 x 107 / 14. 6.6 x 107 / 15. 3.9 x 10-7
16. 8.3 x 10-7 / 17. 7.3 x 10-5 / 18. 7.9 x 109
19. 7.3 x 108 / 20. 1.7 x 1012 / 21. 2.5 x 10-8
22. 5.23 x 10-3 / 23. 4.32 x 10-7 / 24. 7 x 1010
Multiplication –Division -
1st Multiply the numbers1st Divide the numbers
2nd Add the exponents and rewrite it2nd subtract the exponents and rewrite it
3rd Rewrite as scientific notation3rd Rewrite as scientific notation
1. (2 x 103)(4x104) / 2. (6 x 105)(7 x 106) / 3. (5.5 x 107)(4.2 x 104)4. (3.45 x 107) x (6.25 x 105) / 5. (2.33 x 106) x (8.19 x 103) / 6. 3.5 x 108)x( 6.6 x 104)
7. (4 x 106) (2 x 104) / 8. (9 x 108) (2 x 106) / 9. (3 x 107) (8 x 104)
10. (6.8 x 103) x (4.54 x 106) / 11. (2.9 x 108) / (1.3 x 106) / 12. (4.8 x 106)÷(1.2 x 103).
13. (4.3 x 105)(2 x 107) / 14. (4.8 x 106)×(1.2 x 103) / 15. 7.5 x 107)x( 2.6 x 109)
16. (2.8 x 103)(7X109) / 17. (6.8 x 105)(4.2 x 104) / 18. (7.5 x 104)(4.9 x 106)
19. (6.5 x 108) x (6.8 x 106) / 20. (7.33 x 109) x (8.9 x 109) / 21. 2.5 x 108)x( 8.6 x 107)
22. (4.3 x 108) (3X103) / 23. (9.5 x 1010) (5 x 105) / 24. (2 x 1012) (8 x 105)
25. (5.8 x 104) x (6.54 x 104) / 26. (6.9 x 108) / (1.7 x 108) / 27. (6.0 x 108)÷(1.2 x 103).
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/ 3. Which expression represents in simplest form?
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13. What is half of ?
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1) 2) 3) 4) / 15. The quotient of ,is
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16. The expression , is equivalent to
1) 2) 3) 4) / 17. When is divided by , the quotient is
1) 2) 3) 4) / 18. Which expression represents in simplest form?
1) 2) 3) 4)
19. The expression is equivalent to
1) 2) 3) 4) / 20. Which expression represents in simplest form?
1) 2) 3) 4) / 21. Which expression represents in simplest form?
1) 2) 3) 4)
22. The expression is equivalent to
1) 2) 3) 4) / 23. The expression is equivalent to
1) 2) 3) 4) / 24. Simplify:
25. Which expression is equivalent to ?
1) /
2) /
3) /
4) /
/ 26, Expressed in simplest form, is equivalent to
1) /
2) /
3) /
4) /
/ 27. The expression is equivalent to
1) /
2) /
3) /
4) /
28. The expression is equivalent to
1) /
2) /
3) /
4) /
/ 29. The product of and is
1) /
2) /
3) /
4) /
/ 30. If , then is equivalent to
1) /
2) /
3) / 1000
4) / 0
31. The expression is equivalent to
1) /
2) /
3) /
4) /
/ 32. The expression is equivalent to
1) /
2) /
3) /
4) /
/ 33. The expression is equivalent to
1) /
2) /
3) /
4) /
1. The expression is equivalent to
1) x0 2) 2 3) x2 4) -2x4 / 2. Which expression is equivalent to
-3x(x - 4) -2x(x +3)?
1) -x2 - 1
2) -x2 + 18x
3) -5x2 - 6x
4) -5x2 + 6x / 3. The sum of and can be expressed as
1) /
2) /
3) /
4) /
4. The sum of and is
1) /
2) /
3) /
4) /
/ 5. The sum of and is
1) /
2) /
3) /
4) /
/ 6. What is the sum of and ?
1) /
2) /
3) /
4) /
7. What is the sum of and ?
1) /
2) /
3) /
4) /
/ 8. The sum of and is
1) /
2) /
3) /
4) /
/ 9. What is the sum of and ?
1) /
2) /
3) /
4) /
10. The expression is equivalent to
1) /
2) /
3) /
4) /
/ 11. The expression is equivalent to
1) /
2) /
3) /
4) /
/ 12. The expression is equivalent to
1) /
2) /
3) /
4) /
13. 13. When is subtracted from , the difference is
1) /
2) /
3) /
4) /
/ 14. When is subtracted from , the difference is
1) / 0
2) /
3) /
4) /
/ 15. When is subtracted from , the difference is
1) /
2) /
3) /
4) /
16. When is subtracted from , the result is
1) /
2) /
3) /
4) /
/ 17. When is subtracted from , the result is
1) /
2) /
3) /
4) /
/ 18. If is subtracted from , the difference is
1) /
2) /
3) /
4) /
19. Subtract from . / 20. When is subtracted from , the result will be
1) /
2) /
3) /
4) /
/ 21. When is subtracted from , the result is
1) /
2) /
3) /
4) /
22. If is subtracted from , the result is
1) /
2) /
3) /
4) /
/ 23. When is subtracted from , the result is
1) /
2) /
3) /
4) /
/ 24. If is subtracted from , the result is
1) /
2) /
3) /
4) /
25. What is the product of and ?
1) /
2) /
3) /
4) /
/ 26. What is the product of and?
1) /
2) /
3) /
4) /
/ 27. What is the product of and ?
1) /
2) /
3) /
4) /
28. What is the product of and ?
1) /
2) /
3) /
4) /
/ 29. The expression is equivalent to
1) /
2) /
3) /
4) /
/ 30. The expression is equivalent to
1) /
2) /
3) /
4) /
31. The expression is equivalent to
1) /
2) /
3) / 3
4) /
/ 32. When is divided by , the result is
1) /
2) /
3) /
4) /
/ 33. What is divided by ?
1) /
2) /
3) /
4) /
34. When is divided by , the quotient is
1) /
2) /
3) /
4) /
/ 35. The expression
1) /
2) /
3) /
4) /
/ 36. If , the expression is equivalent to
1) /
2) / 2
3) /
4) / 4
37. Which expression represents in simplest form?
1) /
2) /
3) /
4) /
/ 38. Which polynomial is the quotient of ?
1) /
2) /
3) /
4) /
/ 39. Express in simplest form:
4 40. Which value of x makes the expression undefined?
1) /
2) /
3) / 3
4) / 0
/ 41. For which value of x is the expression undefined?
1) / 0
2) / 2
3) /
4) / 4
/ 42. For which value of x is the expression undefined?
1) /
2) / 2
3) / 7
4) / 0
43. For which value of m is the expression undefined?
1) / 1
2) / 0
3) / 3
4) / -3
/ 44. For which value of x is the expression undefined?
1) /
2) / 2
3) / 3
4) / 0
/ 45. For which value of x is the expression undefined?
1) /
2) / 2
3) / 0
4) / 6
46. For which value of x is the expression undefined?
1) / 1
2) /
3) / 5
4) /
/ 47. Which value of n makes the expression undefined?
1) / 1
2) / 0
3) /
4) /
/ 48. For which value of x will the fraction be undefined?
1) /
2) / 2
3) / 0
4) /
49. For which value or values of n is the expression undefined?
1) / 1, only
2) / , only
3) / 1 and
4) / 0
/ 50. For which value of x is undefined?
1) /
2) / 0
3) / 3
4) / 4
/ 51. The function is undefined when the value of x is
1) / 0 or 3
2) /
3) / 3, only
4) /
52. The algebraic expression is undefined when x is
1) / 0
2) / 2
3) / 3
4) / 9
/ 53. Which value of x makes the expression undefined?
1) /
2) / 2
3) / 3
4) /
/ 54. For which set of values of x is the algebraic expression undefined?
1) /
2) /
3) /
4) /
1. What is the product of and written in scientific notation?
1) /
2) /
3) /
4) /
/ 2. What is the product of 12 and expressed in scientific notation?
1) /
2) /
3) /
4) /
/ 3. What is the product of , , and expressed in scientific notation?
1) /
2) /
3) /
4) /
4. What is the quotient of and ?
1) /
2) /
3) /
4) /
/ 5. The quotient of and expressed in scientific notation is
1) / 4,000
2) / 40,000
3) /
4) /
/ 6. If is divided by , the result is
1) / 1
2) / 0.01
3) /
4) /
7. What is the value of in scientific notation?
1) /
2) /
3) /
4) /
/ 8. If the mass of a proton is gram, what is the mass of 1,000 protons?
1) / g
2) / g
3) / g
4) / g
/ 9. If the number of molecules in 1 mole of a substance is , then the number of molecules in 100 moles is
1) /
2) /
3) /
4) /
10. In 1995, the federal government paid off one-third of its debt. If the original amount of the debt was $4,920,000,000,000, which expression represents the amount that was not paid off?
1) /
2) /
3) /
4) /
/ 11. Two objects are centimeters apart. A message from one object travels to the other at a rate of centimeters per second. How many seconds does it take the message to travel from one object to the other?
1) /
2) /
3) /
4) /
/ 12. The distance from Earth to the imaginary planet Med is miles. If a spaceship is capable of traveling 1,420 miles per hour, how many days will it take the spaceship to reach the planet Med? Round your answer to the nearest day.
1