0. Review of Algebra

Factor by any method. See Examples 1–7. $1000x^3+343y^3$

Factor completely, or state that the polynomial is prime. 16x^2-40x+25

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8.

$7(5t+3{)}^{-\frac{5}{3}}+14(5t+3{)}^{-\frac{2}{3}}-21(5t+3{)}^{\frac{1}{3}}$

Factor out the greatest common factor. $18x+27$

Work each problem. Which of the following is the correct factorization of x³+8?

A. (x+2)³

B. (x+2)(x²+2x+4)

C. (x+2)(x²-2x+4)

D. (x+2)(x²-4x+4)

In Exercises 11–16, factor by grouping. x³+6x²−2x−12

Factor each trinomial, if possible. See Examples 3 and 4. (a-3b)²-6(a-3b)+9

Factor out the greatest common factor from each polynomial. See Example 1. 5(a+3)³-2(a+3)+(a+3)²

In Exercises 39–48, factor the difference of two squares. 16x⁴−81

In Exercises 1–10, factor out the greatest common factor. x²(2x+5)+17(2x+5)

In Exercises 65–92, factor completely, or state that the polynomial is prime. x²y−16y+32−2x²

Factor each trinomial, if possible. See Examples 3 and 4. 9m²n²+12mn+4

Factor each polynomial. See Example 7. $a^4-2a^2-48$