0. Review of Algebra

In Exercises 1–68, factor completely, or state that the polynomial is prime. x² − 12x + 36 − 49y²

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

In Exercises 23–48, factor completely, or state that the polynomial is prime.8x² - 8y²

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.x² + xy + y²

In Exercises 23–34, factor out the negative of the greatest common factor.−2x² + 6x − 14

Concept Check When directed to completely factor the polynomial 4x^2y^5-8xy^3,a student wrote 2xy^3(2xy^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 1–68, factor completely, or state that the polynomial is prime. 4x² + 25y²

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.x² − xy + y²

Concept Check Kurt factored 16a^2-40a-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?

In Exercises 23–34, factor out the negative of the greatest common factor.−5y² + 40x

In Exercises 1–68, factor completely, or state that the polynomial is prime. 12x³y − 12xy³

In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication.a² − 18ab + 45b²

Factor each polynomial by grouping. See Example 2. 10ab-6b+35a-21

In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.30. x² - 1/3x