Advanced Algebra: Chapter 6 Review
Name__________________________
Simplify the following. All work must be shown for full credit.
y12
7
8
1. y  y
2. 5
y
a  b c
5
4.
7 3
a 2 b7 c8
63a 2 bc
7.
9abc3


5. 12abc 4a 2 b3
 x 7 y9 z 2 
8. 18.  11 5 
 xy z 

3
3.
1
x 19
 
6. 4x 2 y
2
 3x 8 y2 
9. 
2 
 12xyz 
0
Learning Target: I can multiply and simplify monomials and expressions using powers.
Learning Target: I can divide and simplify monomials and expressions using powers.
Learning Target: I can simplify monomials that have negative exponents.
Learning Target: I can simplify monomials that have a power of zero.
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Advanced Algebra: Chapter 6 Review
Find the degree of each polynomial.
10. 2 x3  x  3x 7
11. 4 xy  2 y  5 x 2
12. 5cx  10c 2 x3  15cx 2
degree___________
degree___________
degree___________
Learning Target: I can find the degree of a polynomial.
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Solve by long division.
Solve by synthetic division.
13. ( x 2  3x  2)  ( x  7)
14. ( x 4  2 x3  x  1)  ( x  1)
Learning Target: I can divide polynomials using long division.
Learning Target: I can divide polynomials using synthetic division.
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Simplify the following polynomials.

 
15. x 3x 5 7 x 2  2x  9


 
16. 5 2y2 3y 2 8 3y2  4y 2

Learning Target: I can simplify polynomials.
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Advanced Algebra: Chapter 6 Review
Factor each expression by GCF.
17. 5m 3n  35m2 n 3
18. 2d 2 e2  8d 6 e6
Learning Target: I can factor an expression by the Greatest Common Factor
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Factor each expression by Grouping. Check using FOIL.
19. 2x 2 y  6xy  x  3
20. 4k  12  k 2  3k
Learning Target: I can factor and expression by Grouping.
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Factoring each polynomial, if possible. If the polynomial cannot be factored, write prime. Remember:
Try to take out a GCF.
21. 7a 2  22a  3
22. x 4  13x 2  36
23. 12 y 2  27
Advanced Algebra: Chapter 6 Review
24. 4ab 4  16ab2
25. 128 y 3  16
26. r 4  125r
Learning Target: I can factor a trinomial.
Learning Target: I can factor a polynomial by a difference of squares.
Learning Target: I can factor a polynomial by sum of two cubes.
Learning Target: I can factor a polynomial by difference of two cubes.
Chapter 6 Review Key
1.
8.
𝑦5
z9
x18 y6
2. 𝑦 7
9. 1
3. 𝑥19
10. 7
4.
11. 2
−𝑎3
𝑐5
12. 5
68
16. −14𝑦 2 − 17𝑦 + 6
19. (2xy – 1) (x + 3)
20. (4 + k) (k + 3) 21. (7a + 1) (a + 3)
24. 4𝑎𝑏 2 (𝑏 + 2)(𝑏 − 2)
26. 𝑟(𝑟 − 5)(𝑟 2 + 5𝑟 + 25)
6. 16𝑥 4 𝑦 2
7. −7𝑎𝑐 4
1
14. 𝑥 3 − 3𝑥 2 + 3𝑥 − 2 + 𝑥+1
13. 𝑥 − 10 + 𝑥+7
15. 4𝑥 2 − 9𝑥 + 63
23. 3(2y + 3) (2y – 3)
1
5. −48𝑎3 𝑏 4 𝑐
17. 5𝑚2 𝑛(𝑚 + 7𝑛2 )
18. 2𝑑 2 𝑒 2 (1 − 4𝑑4 𝑒 4 )
22. (x + 3) (x – 3) (x – 2) (x + 2)
25. 16(2𝑦 − 1)(4𝑦 2 + 2𝑦 + 1)