Algebra II
Chapter 6 Review
Rewrite each polynomial in standard form. Then identify the leading coefficient, degree, and number of
terms. Name the polynomial by its degree.
3x5+4x2-5
Leading Coefficient: 3
Degree: 5
# of terms: 3
Name: Quintic
1. 4x2 + 3x5 - 5
3. 1 + 5x3 + x2 - 3x 5x3+x2-3x+1
Leading Coefficient: 5
Degree: 3
# of terms: 4
Name: Cubic
2. 7 + 13x
13x+7
Leading Coefficient: 13
Degree: 1
# of terms: 2
Name: Linear
4. 8x + 2x4 - 5x3
2x4-5x3+8x
Leading Coefficient: 2
Degree: 4
# of terms: 3
Name: Quartic
Add or subtract. Write your answer in standard form.
5. (3x2 + 1) + (4x2 + 3)
7x2+4
7. (11x2 + x3 + 7) + (5x3 + 4x2 - 2x)
6x3+15x2-2x+7
6. (9x3 - 6x2 ) - (2x3 + x2 + 2)
7x3-7x2-2
8. ( x5 - 4x4 + 1) - (-7x4 + 11)
x5+3x4-10
Find each product.
9. 2y (4x2 + 7xy)
8x2y+14xy2
11. (x+3)(x-2)(x+4)
x3+5x2-2x-24
10. (a + b) (3ab + b2)
3a2b+4ab2+b3
12. (2x - 3) ( x3 - x2 + 3x + 5)
2x4-5x3+9x2+x-15
13. 2x3y4 (2xy4)2
14. m2n4 (3xy2)-3
𝑚 2 𝑛4
27𝑥 3 𝑦 6
8x5y12
15.
(2
16.
)
2
𝑦
4𝑥 3
4
(2
)
𝑦10
4𝑥
Expand each expression.
17. (x - 3)4
18. (x + 2y)3
x4-12x3+54x2-108x+81
x3+6x2y+12xy2+8y3
Divide.
19. (6y2 + 13y - 8) ÷ (2y - 1)
3y+8
20. (6x2+x-15) ÷ (2x - 3)
3x+5
21. (3x3 + 11x2 + 11x + 15) ÷ (x + 3)
3x2+2x+5
22. (8x3-13x2-7x+2) ÷ (x - 2)
8x2+3x-1
Use synthetic substitution to evaluate the polynomial for the given value.
23. P (x) = x3 + 2x2 - 5x + 6 for x = -1
24. P (x) = x4 + x2 + x - 6 for x = 2
16
12
Factor Completely
25. 3t3 - 21t2 - 12t
3t(t2-7t-4)
27. y3 + 7y2 + 2y + 14
(y2+2)(y+7)
29. a6 + 125
26. 16y2 - 49
(4y-7)(4y+7)
28. 6x3-9x2+2x-3
(3x2+1)(2x+3)
30. 8x3-27y3
(a2+5)(a4-5a2+25)
(2x-3y)(4x2+6xy+9y2)
Factor using the Factor Theorem
31. x3-10x2+13x+24
(x+1)(x-3)(x-8)
33. 3x3-7x2-2x+8
(x+1)(x-2)(3x-4)
32. x3-10x2+x+120
(x+3)(x-5)(x-8)
34. 6x3-19x2-21x+4
(x+1)(x-4)(6x-1)