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Algebra 1 8.6 Choosing a Factoring Method

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Learning Targets Language Goal: Students will be able describe an appropriate method for factoring a polynomial. Math Goal: Students will be able to combine methods for factoring a polynomial. Essential Question: Why is it important to have multiple methods to factor polynomials?

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Warm-up

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Example Type 1: Determining Whether a Polynomial Is Completely Factored Tell whether the polynomial is completely factored. If not, factor it. A. 2x(x² + 4) B. (2x + 6)(x + 5) C. 5x²(x – 1)

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Example Type 1: Determining Whether a Polynomial Is Completely Factored Tell whether the polynomial is completely factored. If not, factor it. D. (4x + 4)(x + 1) E. 3x²(6x – 4)F. (x² + 1)(x – 4)

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Example Type 1: Determining Whether a Polynomial Is Completely Factored Tell whether the polynomial is completely factored. If not, factor it. G. 3x(9x² – 4) H. 2(x³ – 2x² – 8x)

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Factoring Polynomials Step 1: Check for a greatest common factor. Step 2: Check for a pattern that fits the difference of two squares or a perfect-square trinomial. Step 3: - To factor x² + bx + c, look for two numbers whose sum is b and whose product is c. (Product Sum Method) - To factor ax² + bx + c, check factors of a and factors of c in the binomial factors. The sum of the products of the outer and inner terms should be b. (Boston Method Step 4: Check for common factors

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Example Type 2: Factoring by GCF and Recognizing Patterns

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Factor completely. Check your answer. C. 2x²y – 2y³D. 10x² + 48x + 32

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Example Type 2: Factoring by GCF and Recognizing Patterns

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Example Type 3: Factoring by Multiple Methods Factor each polynomial completely. A. 2x² + 5x + 4 B. 3n – 15n³ + 12n²

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Example Type 3: Factoring by Multiple Methods

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1. D2. E. 3. A4. B5. C

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Lesson Quiz

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