0. Review of Algebra

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

$(3r+1{)}^{-\frac{2}{3}}+(3r+1{)}^{\frac{1}{3}}+(3r+1{)}^{\frac{4}{3}}$

Concept Check When directed to completely factor the polynomial $4x^2{y}^5-8x{y}^3$,a student wrote $2x{y}^3(2x{y}^2-4)$. When the teacher did not give him full credit, he complained because when his answer is multiplied out, the result is the original polynomial. Give the correct answer.

In Exercises 65–92, factor completely, or state that the polynomial is prime. 20y⁴−45y²

Find all values of b or c that will make the polynomial a perfect square trinomial. 4z²+bz+81

Factor the polynomial.

$4x^2-19x+12$

Factor each perfect square trinomial. $64x^2-16x+1$

Concept Check Kurt factored 16a²-40a-6a+15 by grouping and obtained (8a-3)(2a-5). Callie factored the same polynomial and gave an answer of (3-8a)(5-2a). Which answer is correct?

Factor and simplify each algebraic expression. $16x^{-\frac{3}{4}}+32x^{\frac{1}{4}}$

Factor and simplify each algebraic expression.$[12x^{-\frac{1}{2}}+6x^{-\frac{3}{2}}]$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $4x^3-12x^2=9x-27$

Factor the polynomial.

$x^2-2x-15$

In Exercises 103–114, factor completely. x⁴−5x²y²+4y⁴