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# Algebra: Solve, Simplify & Factorize

1. If an expression has two terms, check to see whether the problem type is the -------- of two squares, the sum of two ------ , or the ----------- of two cubes.

2. If an expression has four or more terms, try factoring it by--------------.

3. Factor the polynomial. bc + b + cd + d

4. Factor the polynomial. 64x9 - y3

5. Factor the expression.

6. Factor the polynomial. 4z2 - 361t2

7. Factor the polynomial. a2x2 + b2y2 + b2x2 + a2y2

8. Factor the polynomial. x4 - x4y4

9. Factor the polynomial.

HW5.8

1. Solve the following equation. (Enter solutions from smallest to largest. If a solution has a multiplicity of two, enter it in consecutive answer boxes.)
x2 + 25x + 114 = 0
x =
x =

2. Solve the following equation. (Enter solutions from smallest to largest. If a solution has a multiplicity of two, enter it in consecutive answer boxes.)
x2 - 31x + 228 = 0
x =
x =

3. Find all x that will make f(x) = 0. (Enter solutions from smallest to largest.)

x =
x =

4. Use grouping to help solve the following equation. (Enter solutions from smallest to largest.)

s =
s =
s =

5. Solve the following equation. (Enter solutions from smallest to largest. If a solution has a multiplicity of two, enter it in consecutive answer boxes.)
x2 - 8x = 0
x =
x =

6. Solve the equation. You will need to use the factoring techniques that we discussed throughout this chapter.
w2 - 3w = 54
w = (smaller value)
w = (larger value)

7. Solve the equation. You will need to use the factoring techniques that we discussed throughout this chapter.
5n3 = 180n
n = (smallest value)
n =
n = (largest value)

8. Solve the equation. You will need to use the factoring techniques that we discussed throughout this chapter.
x2 = 81
x = (smaller value)
x = (larger value)

1. Find the degree of the following polynomial.

2. Consider the polynomial function P(x) = 8x2 + x + 1 and find the following value.
f(-2)

3. Find the value when x = 10 and y = -3.
x3 + y3

4. Simplify the expression.
3wxy - 6wxy

5. Perform the operation.

6. Simplify the following expression.

7. Find the product.

8. Find the product.
(-3a2ab2)3(-3ab2b2)

9. Find the product.

10. Find the product.
(4y + 4z)(2y - 3z)

11. Find the product.

12. Find the prime-factored form of the following number.
432

13. Factor the expression, if possible. Otherwise, enter PRIME.
92x2 + 76x

14. Factor the expression.

15. Factor the expression.
81x4 - 25y2

16. Factor the expression.

17. Factor the trinomial. Factor out all common monomials first (including -1 if the lead coefficient is negative). If the trinomial is prime, enter PRIME.

18. Factor the trinomial. Factor out all common monomials first (including -1 if the lead coefficient is negative). If the trinomial is prime, enter PRIME.

19. Factor the following expression.

20. Factor the polynomial.
bc + b + cd + d

21. Factor the polynomial.
343x9 - y3

22. Solve the following equation. (Enter solutions from smallest to largest. If a solution has a multiplicity of two, enter it in consecutive answer boxes.)
x2 + 19x + 34 = 0
x =
x =

23. Solve the following equation. (Enter solutions from smallest to largest. If a solution has a multiplicity of two, enter it in consecutive answer boxes.)
x2 - 19x + 70 = 0
x =
x =