Algebra 1

8.6 Choosing a Factoring Method

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?

Warm-up

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)

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)

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)

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 MethodStep 4: Check for common factors

F act or i ng a P olynomi al

Is there a GCF?

No Yes

Is there a quadratic left? (Degree 2)

No Yes How many terms are

left?

3 2

Are they subtracted & perfect squares?

What value does a have?

No Yes

a ≠ 1 a = 1

Difference of Two Squares

Product Sum Rule Boston Method

Example Type 2: Factoring by GCF and Recognizing Patterns

Factor completely. Check your answer.A. B.

Example Type 2: Factoring by GCF and Recognizing Patterns

Factor completely. Check your answer.C. 2x²y – 2y³ D. 10x² + 48x + 32

Example Type 2: Factoring by GCF and Recognizing Patterns

Factor completely. Check your answer.E.

Example Type 3: Factoring by Multiple Methods

Factor each polynomial completely.A. 2x² + 5x + 4 B. 3n – 15n³ + 12n²

Example Type 3: Factoring by Multiple Methods

Factor each polynomial completely.C. D.

Example Type 3: Factoring by Multiple Methods

Factor each polynomial completely.E. F.

Example Type 3: Factoring by Multiple Methods

Factor each polynomial completely.G.H.

Example Type 3: Factoring by Multiple Methods

Factor each polynomial completely.I. J.

Example Type 3: Factoring by Multiple Methods

Factor each polynomial completely.K. L.

𝑎𝑏−𝑎𝑐=𝑎(𝑏−𝑐)6 𝑥2 𝑦+10𝑥𝑦 2=2 𝑥𝑦 (3 𝑥+5 𝑦 )

𝑎2−𝑏2=(𝑎−𝑏)(𝑎+𝑏)𝑥2−9 𝑦2=(𝑥−3 𝑦 )(𝑥+3 𝑦 )

𝑎𝑥+𝑏𝑥+𝑎𝑦+𝑏𝑦=𝑥 (𝑎+𝑏 )+𝑦 (𝑎+𝑏)=(x+ y)(a+b)2 𝑥3+4 𝑥2+𝑥+2 𝑦=2 𝑥2 (𝑥+2 )+1 (𝑥+2 )=( x+2)(2𝑥2+1)

1. D 2. E. 3. A 4. B 5. C

Lesson Quiz