1.Students Will Be Able to Factor a Polynomial Using the Greatest Common Factor
Algebra 1 Unit 6
1.Students will be able to factor a polynomial using the greatest common factor.
(Section 8.2)
Worksheet 11 - 20
2.Students will be able to factor using difference of two squares. (Section 8.7)
Page 40713 – 30
Worksheet 21 – 29
*Quiz 1
3.Students will be able to factor trinomials of the form x2 + bx + c (Section 8.5)
Page 3976 – 38 even, 44 – 54 even
4.Students will be able to factor trinomials of the form ax2 + bx + c (Section 8.6)
Page 4012 – 26 even
*Quiz 2
5.Students will be able to factor using all the different types of factoring.
Worksheet 51 - 21
6.Students will be able to solve quadratic equations by factoring and using the
zero-product property. (Section 9.5)
Worksheet 61 – 23
7.Students will be able to solve quadratic equations that apply to physical problems.
(Section 9.5)
Page 45421 - 24
8.Students will be able to sketch factorable quadratics, knowing that the roots are the x-intercepts and knowing the direction of opening.(Sections 9.1, 9.2)
Worksheet 71 – 30
*Quiz 3
Review
Review 11 – 36
Review 21 - 20
Worksheet 1
Factor completely.
1.x2– 4x2.y2 + 8y3.2x2 + 2x
4.3y2– 3y5.3y2 + 6y + 66.6x2 + 12
7.14m4– 12m8.32x5– 60x49.2x2 + 2x – 8
10.x3y + 6x2y11.40x4y2– 24x2y12.15y2– 5y
13.77x – 84y14.ax + bx15.5x2 + 10x + 30
16.15x3y + 17x417.14x3y3– 21x2y + 35xy18.12m5n2 + 9m4n + 6m3n2
Multiple Choice:
19.Which shows the complete factorization of 12x3y2 + 18x2y4 ?
A.6(2x3y2 + 3x2y4)B.x2y2(12x + 18y2)
C.6xy(2x2y+ 3xy3)D.6x2y2(2x + 3y2)
20.Which shows the complete factorization of 6x3 + 4x2 + 2x ?
A.x(6x2 + 4x + 2)B.2x(3x2 + 2x)
C.2x(3x2 + 2x + 1)D.2(3x3 + 2x2 + x)
Worksheet 2
Tell whether each binomial is the difference of two squares. If it is, factor it. If it is not write ‘prime’.
1.x2 + 92.x2– 103.x2– 81
4.2x2– 255.x2 + 646.x2 + y2
Factor the following completely:
7.x2– 18.4x2– 81y29.25 – x2
10.9y2– 16x211.100 – 49x212.x2– 1
13.x2– 114.x2– 15.– y2
Factor the following completely.
1)First factor out the greatest common factor.
2)Then factor the remaining using difference of two squares.
16.6x2– 6y217.5x2 – 2018.x2y – 9y
Factor the following completely.
1)First factor out the greatest common factor.
2)Then factor the remaining using difference of two squares.
19.4x2– 420.50 – 2x221.x3– 36x
22.9x2– 3623.27 – 3x224.2x3– 200x
25.9x2– 81
Select the correct multiple choice response.
26.Which of the following is one of the factors of 4x2– 1 ?
A.x + 2B.2x + 1C.4x + 1D.x + 1
27.Which of the following shows the complete factorization of 9x2– 9 ?
A.9(x2– 1)B.(3x + 3)(3x – 3) C. 3(3x2– 3)D. 9(x + 1)(x – 1)
28.The product of two binomials is x2 – 9. If one of the binomials is x + 3, what is
the other binomial?
A.x – 3B.x + 3C.x + 1D.x – 9
29.Which shows the complete factorization of 100 – x2?
A.(x + 10)(x – 10)B.(x – 10)2
C.(10 – x)(10 + x)D.(10 – x)2
Worksheet 5
Factor the following completely:
1. x2 + 4x + 42. x2 – 14x + 49 3. x2 + 18xy + 81y2 4. 36x2 – 12x + 1
5. 9x2 – 12x + 46. 25x2 – 40xy + 16y27.9x2 – 81 8.16x2 – 64
9.36 – 4x210.4x2 – 411.16 – 16x2 12. 9 – 36x2
13.100 – 100x214.64 – 4x215.4x2 – 16
16.2x2 + 8x – 1017.3x2 + 30xy + 63y2 18.4x2 + 12x + 8
Select the correct multiple choice response:
19.Which is a factor of x2 – 9x + 8?
A.x – 9B.x – 8C.x + 1D.x + 8
20.What is the complete factorization of 9x2 – 9?
A. (3x – 3)2B. (3x + 3)(3x – 3) C.9(x2 – 1)D. 9(x + 1)(x – 1)
21.Which is a factor of 4y2 + 12y + 9?
A.4x + 9B.2x + 9C.2x + 3D.4x + 3
Worksheet 6
Find the solutions for the quadratic equations:
1.x2 + 5x – 6 = 02.x2 – 18x – 40 = 03.x2 – 6x + 8 = 0
4.x2 + 11x + 28 = 05.x2 + 4x – 32 = 06.x2 – 13x = 48
7.x2 – 15x = 168.x2 + 7x = 189.x2 + 3x = 54
10.3x2 + 7x + 2 = 011.2x2 + 5x + 3 = 012.3x2 – 8x + 5 = 0
13.9x2 + 6x + 1 = 014.3x2 + 7x = 615.4x2 + 4x = 3
16.5x2 + 4x = 117.6x2 + 2x = 418.3x2 – 3x = 18
For the following problems write an equation and then solve algebraically.
19.If x2 is added to x, the sum is 12. Find the possible values of x.
20.If x2 is added to 5x, the sum is –6. Find the possible values of x.
21.If x2 is added to 3x, the sum is 10. Find the possible values of x.
Select the correct multiple choice response:
22.What are the solutions for the quadratic equation x2 + 8x = 20?
A.2, 10B.2, – 10C.–2, – 10D.–2, 10
23.What are the solutions for the quadratic equation 2x2 + 4x = 30?
A.5, –3B.2, 5, –3C.–5, 3D.–2, – 5, 3
Worksheet 8
Sketch the following. Label the x-intercepts on your graph.
1. y = (x + 3)(x – 5)2. y = (x + 2)(x + 6)3.y = (x + 4)(x – 4)
4.y = – (x – 1)(x + 3)5.y = – x (x + 6)6. y = – (x – 6)(x + 6)
7.y = (2x + 1)(x – 4)8.y = – (3x – 2)(x + 2)
Factor the following. Then sketch and label the x-intercepts on your graph.
9.y = x2– 410.y = x2 + 6x + 511.y = x2– 6x – 7
Factor the following. Then sketch and label the x-intercepts on your graph.
12.y = x2– 3x13.y = – (x2– 1)14.y = –(x2– 4x – 12)
15.y = – (x2 + 2x)16.y = – (x2 + 3x – 4)17.y = 2x2 + 3x + 1
Select the correct multiple choice response.
18.Which one of the following could be the graph of y = (x + 4) (x – 2) ?
A) B) C) D)
19.Which one of the following could be the graph of y = – x (x + 5) ?
A) B) C) D)
20.Which one of the following could be the graph of y = x2– 9 ?
A) B)C)D)
21.State the direction of opening for y = – x (x + 6)
A)UpB)DownC)RightD)Left
22.State the direction of opening for y = x2 + 5x + 4
A)UpB)DownC)RightD)Left
For problems 23 – 30 select the graph from letters A – H that represents the equation.
23.y = (x + 2)(x – 4)24.y = (x + 2)(x + 4)
25.y = – (x – 2)(x + 4)26.y = (x – 2)(x – 4)
27.y = – (x – 2)(x – 4)28.y = – (x + 2)(x + 4)
29.y = (x – 2)(x + 4)30.y = – (x + 2)(x – 4)
A.B.C.
D.E.F.
G.H.
Review 1
Give the complete factorization of the following:
1.x2 + 12x + 362.x2 + 5x – 363.x2 – 16x + 64
4.x2 – 20xy + 100y25.x2 – 8x – 206.x2 – 22x + 121
7.x2 – 9x + 188.9x2 + 12x + 49.3x2 – 20x – 7
10.5x2 + 13y – 611.25x2 + 40x + 1612.4x2 – 28xy + 49y2
13.4x2 + 11xy + 7y214.x2 – 3615.x2 –
16.100 – x217. – x218. – x2
19.36x2 – 3620.49 – 49x221.100x2 – 25
22.2x2 – 8xy + 8y223.2x2 – 14xy + 20y224.3x2 + 6xy + 3y2
25.2x2 + 16x + 32
Give the solutions for the quadratic equations:
26.x2 – 3x – 28 = 027.x2 + 4x = 1228.x2 – 5x = 6
29.2x2 + 14x = – 2430.2x2 + 3x = –131.2x2 – 8x = 42
32.If x2 is added to 2x the result is 35. Write an algebra equation and solve for the
values of x.
33.If x2 is added to 4x the result is 45. Write an algebra equation and solve for the
values of x.
Graph the following by plotting the x-intercepts and opening the parabola in the correct direction.
34.y = x2 + 2x – 335.y = x2 – 436.y = –x(x – 3)
Review 2
In problems 1 – 15, select the correct multiple choice response:
1.What is the complete factorization of 9x2 – 24x + 16?
A. (3x + 4)2B. (3x + 4)(3x – 4)C. (9x – 4)(x – 4)D. (3x – 4)2
2.What is the complete factorization of 16x2 – 4 ?
A. (4x + 2)(4x – 2) B. 4(2x + 1)(2x – 1)C. 4(2x – 1)2D. 4(4x2 – 1)
3.Which is a factor of x2 – 20x + 100 ?
A. x – 10B. x + 10C. x – 100D. x – 50
4.Which is a factor of 3x2 + 11x – 4 ?
A. 3x + 1B. 3x – 1C. x – 4D. 3x – 4
5.Which of the following shows 2x2 – 16xy + 32y2 factored completely?
A. (2x – 4y)(x – 8y)B. 2(x – 4y)(x – 4y)
C. (2x – 16y)(x –2y)D. 2(x – 2y)(x – 8y)
6.What is the complete factorization of x2 – 3x – 40 ?
A. (x – 8)(x + 5)B. (x – 2)(x + 20) C. (x – 10)(x + 4) D. (x – 2)(x – 20)
7.What is the complete factorization of 100 – 100x2 ?
A. 100(x2 – 1) B. 100(1 – x)2C. (10 + 10x)(10 – 10x) D. 100(1 + x)(1 – x)
8.What is the factored form of 2x2 – 16xy + 24y2 ?
A. (2x – 3y)(x – 8y)B. (2x – y)(x – 24y)
C. 2(x – 2y)(x – 6y)D. 2(x – 6y)(x – 6y)
9.What are the solutions for the quadratic equation x2 – 7x – 18 = 0?
A. 9, 2B. –9, –2C. 9, –2D. –9, 2
10.What are the solutions for the quadratic equation x2 + 8x = 20 ?
A. –10, 2B. 10, –2C. –10, –2D. 10, 2
11.What are the solutions for the quadratic equation 2x2 + 10x = – 8 ?
A. 4, 1B. –4, –1C. 2, 4, 1D. –2, –4, –1
12.If x2 is added to 4x the sum is 12. Which of the following could be the
value of x?
A. 8B. 12C. –2D. –6
13.Which of the following could be the graph of y = x2 – 9 ?
A.B.C.D.
14.Which of the following could be the graph of y = –x(x + 2) ?
A.B.C.D.
15.Which of the following could be the graph of y = x2 – 2x – 24 ?
A.B.C.D.
Work the following showing all work.
16.Factor completely: 6x2 + 13x – 5
17.Factor completely: – x2
18.Factor completely: 49x2 + 30xy + 64y2
19.Solve the quadratic equation: x2 – 23x = 50
20.Solve the quadratic equation: x2 + 17x = –42
Algebra 1 Unit 61