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Factoring Polynomials Review: Solve Equations & Factor Completely

Learn how to solve equations by factoring polynomials and factor polynomials completely. Review GCF, binomial, trinomial, and polynomial factoring methods. Check your answers to ensure accuracy.

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Factoring Polynomials Review: Solve Equations & Factor Completely

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  1. Warm Up: Solve the Equation 4x2 + 8x – 32 = 0

  2. 9.6 Factoring Polynomials Review… If it’s an equation, set it equal to zero! Factor out The GCF Left with a Binomial Left with a Trinomial Left with a Polynomial With 4 terms Factor by Grouping Check for Difference of Perfect Squares If a = 1 Make a table prod = c, sum = b If a≠1 Make a table prod = a·c, sum = b

  3. Example 1: Factoring Out the GCF First Factor 10x2 + 48x + 32 completely. Check your answer. 10x2 + 48x + 32 Factor out the GCF. 2(5x2 + 24x + 16) 2(5x + 4)(x + 4)

  4. Example 2: Factoring Factor 8x6y2– 18x2y2 completely. Check your answer. 8x6y2– 18x2y2 Factor out the GCF. 4x4 – 9is the difference of two perfect squares. 2x2y2(4x4– 9) 2x2y2(2x2– 3)(2x2 + 3)

  5. 4x(x2 + 4x + 4) Examples 3 and 4: Factoring Factor each polynomial completely. Check your answer. 4x3 + 16x2 + 16x 2x2y– 2y3 2y(x2–y2) 4x(x + 2)(x + 2) 2y(x + y)(x–y)

  6. Examples 5 and 6: Factoring Factor each polynomial completely. Check your answer. 2b3– 12b2 + 18b 4y2 + 12y– 72 4(y2 + 3y– 18) 2b(b2– 6b + 9) 4(y –3)(y + 6) 2b(b– 3)(b – 3)

  7. Examples 7 and 8: Factoring Factor each polynomial completely. Check your answer. 2x4 + 18 (x4–x2) 2(x4 + 9) x2(x2– 1) x2(x + 1)(x– 1)

  8. Lesson Quiz Solve each equation: 1. 6b3 – 24b2 + 24b=0 2. c2 – 18c + 81 =144 x=0 or x=2 c= –3 or c=21 Factor each polynomial completely. Check your answer. 3.x3 + 4x2 + 3x + 12 4. 4x2 + 16x – 48 4(x + 6)(x– 2) (x + 4)(x2 + 3) 5. 18x2– 3x– 3 6. 18x2– 50y2 3(3x + 1)(2x– 1) 2(3x + 5y)(3x– 5y) 7. 5x –20x3 + 7 – 28x2 (1 + 2x)(1 – 2x)(5x + 7)

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