Factoring Review Algebra 2

Algebra 2 (bell work) Copy down

Tell whether each polynomial is completely factored. If not factor it. A. 3x2(6x – 4) B. (x2 + 1)(x – 5) (x2 + 1)(x – 5) 3x2(6x – 4) 6x2(3x – 2) 6x2(3x – 2) is completely factored. (x2 + 1)(x – 5) is completely factored.

Tell whether the polynomial is completely factored. If not, factor it. A. 5x2(x – 1) B. (4x + 4)(x + 1) 5x2(x – 1) (4x + 4)(x + 1) 5x2(x – 1) is completely factored. 4(x + 1)(x + 1) 4(x + 1)2 is completely factored.

Factor 10x2 + 48x + 32 completely. Check your answer. Check 2(5x + 4)(x + 4) = 2(5x2 + 20x + 4x + 16) = 10x2 + 40x + 8x + 32 = 10x2 + 48x + 32 

 8x6y2 – 18x2y2 Factor 8x6y2 – 18x2y2 completely. Check your answer. 2x2y2(2x2 – 3)(2x2 + 3) Check 2x2y2(2x2 – 3)(2x2 + 3) = 2x2y2(4x4 – 9) = 8x6y2 – 18x2y2 

4x3 + 16x2 + 16x Factor each polynomial completely. Check your answer. Check 4x(x + 2)2 = 4x(x2 + 2x + 2x + 4) = 4x(x2 + 4x + 4) = 4x3 + 16x2 + 16x 

8.6 If none of the factoring methods work, the polynomial is said to be unfactorable. For a polynomial of the form ax2 + bx + c, if there are no numbers whose sum is b and whose product is ac, then the polynomial is unfactorable. Helpful Hint

  9x2 + 3x – 2 Factors of 9 Factors of 2 Outer + Inner 1 and 9 Factor each polynomial completely. 9x2 + 3x – 2 9x2 + 3x – 2 ( x + )( x + )  Factors of 9 Factors of 2 Outer + Inner 1 and 9 1 and –2 1(–2) + 1(9) = 7 3 and 3 3(–2) + 1(3) = –3 –1 and 2 3(2) + 3(–1) = 3  (3x – 1) (3x + 2)

  12b3 + 48b2 + 48b Factor each polynomial completely. Factors of 4 Sum 1 and 4 5 2 and 2 4   a = 2 and c = 2 12b(b + 2)(b + 2) 12b(b + 2)2

  4y2 + 12y – 72 Factor each polynomial completely. 4(y2 + 3y – 18) Factors of –18 Sum –1 and 18 17 –2 and 9 7  –3 and 6 3 4(y – 3)(y + 6)

(x4 – x2) Factor each polynomial completely. x2(x2 – 1) x2(x + 1)(x – 1)

HW 5.3- #37-45, 48-54 Solve by factoring