Int Alg II Review over 5.1-5.4Name
Determine the end behavior of the graph of each polynomial function.
1. y = 5x3 2x2+ 1 1A. y = 1 + 2x + 4x38x4
Determine the sign of the leading coefficient and the degree of the polynomial function for each graph.
2.
3.
4.
Sign: Sign: Sign:
Degree: Degree: Degree:
Classify each polynomial by degree and by number of terms. Simplify first if necessary.
5. 3x5 6x2 5 +x26. (5x2 + 2x 8) + (5x24x)
Find the zeros of each function. Then graph the function.
7. y = (x + 2)(x + 3)8. y = x(x 1)(x + 3)
Write a polynomial function in standard form with the given zeros.
9. x = 3, 0 10. x = 3, -2, 1
Find the zeros of each function. State the multiplicity of multiple zeros.
11. y = (x 3)2(x + 1) 12. y = x2 + 3x + 2
Find the relative maximum and relative minimum of the graph of each function. Use calculator.
13. f(x) = 3x3 + 10x2 + 6x 3 14. f(x) = x3 + 4x2x +1
15. Reasoning A polynomial function has a zero at x = b. Find one of its factors.
16. The length of a box is 2 times the height. The sum of the length, width, and height of the box is 10 centimeters.
a.Write expressions for the dimensions of the box.
b.Write a polynomial function for the volume of the box. (To start, write the function in factored form).
c.Find the maximum volume of the box and the dimensions of the box that generates this volume.
Find the real or imaginary solutions of each equation. Start by factoring.
17. x3 + 512 = 0 18. x3 + 4x2 − 2x −8 = 0
Find the real or imaginary solutions of each equation by factoring.
19. x4 − 3x2 = −2x2 20. x3 = 9x
Find the real solutions of each equation by graphing.
21. x3 − 3x2 − 9x = −15
22. 2x4 − 2x3 + 4x2 = 3
Write an equation to model each situation. Then solve each equation by graphing.
23. The product of three consecutive integers is 720. What are the numbers?
Divide using synthetic division. Check your answers.
24. (x3 + x214x 27) ÷(x + 3)
25. Determine whether x 4is a factor of x33x24x.
26. Determine whether x + 1 is a factor of x39x2+ 15x + 25.
Divide using synthetic division.
27. (x3 + x214x 27) ÷(x + 3)28. (x315) ÷(x 1)
Use synthetic division and the given factor to completely factor each function.
29. y = 2x3 + 9x2 + 13x + 6; (x + 1)
Use synthetic division and the Remainder Theorem to find P(a).
30. P(x) = 5x312x2 + 2x + 1, a = 3 31. P(x) = x3412, a = 8