Solving Equations by Factoring Revised

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Learn and practice solving equations using factoring and the Zero Product Property.

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Solving Equations by Factoring:

Solving Equations by Factoring Ms. Rineman

Factoring Binomials:

Factoring Binomials Rearranging binomials by removing common factor Variables and numbers can be factored Factoring is backwards of expanding/distributing

Example:

Example Expand: 3(x + 2) = 3(x) + 3(2) = 3x + 6 Factor: (3x + 6) = 3(x) + 3(2) = 3(x + 2)

You Try:

You Try Factor: (5x + 5) 5(x + 1) Factor: (14y 2 + 3y) y(14y + 3) Factor: (4x 2 - 24x) 4x(x - 6)

Difference of Perfect Squares:

Difference of Perfect Squares For a 2 - b 2 = (a - b)(a + b) Example: x 2 – 4 = (x) 2 – (2) 2 = (x – 2)(x + 2) 4x 2 – 25 = (2x) 2 – (5) 2 = (2x – 5)(2x + 5)

Factoring Quadratic Polynomials:

Factoring Quadratic Polynomials Quadratic polynomial looks like ax 2 + bx + c To solve, find two numbers that: Multiply to be the constant term “c” Add to equal “b” the coefficient of x 1

Steps to Factoring:

Steps to Factoring Find “a”, “b”, and “c” in polynomial Write down factor pairs for “c” Which pair adds to be “b”? Substitute factor pairs into two binomials

Example:

Example Factor: x 2 – 11x + 18 a = 1, b = -11, c = 18 Factors of 18: 1 ∙ 18, -1 ∙ -18, 2 ∙ 9, -2 ∙ -9, 3 ∙ 6, -3 ∙ -6

Example Continued:

Example Continued Factors Pairs Sum of Factors (must equal 18) (must equal -9) 1 ∙ 18 1 + 18 = 19 -1 ∙ -18 -1 + -18 = -19 2 ∙ 9 2 + 9 = 10 - 2 ∙ -9 -2 + -9 = -11 3 ∙ 6 3 + 6 = 12 -3 ∙ - 6 -3 + -6 = -9 x 2 – 11x + 18 = (x – 3)(x – 6)

Solving Quadratic Equations by Factoring:

Solving Quadratic Equations by Factoring Solving for “ zeros ” of graph Zeros (x-intercepts): when y = 0 To solve ax 2 + bx + c = 0, Factor Use Zero Product Property to solve

Zero Product Property:

Zero Product Property If ab = 0, then a = 0 or b = 0. If (x – 2)(x – 3) = 0, then (x – 2) = 0 or (x – 3) = 0. Solve for each case. x – 2 = 0 x – 3 = 0 x = 2 OR x = 3

Factoring Polynomials of Degree > 2:

Factoring Polynomials of Degree > 2 Pull out any common factors Factor the simplified polynomial in parentheses

Example:

Example 10x 4 + 15x 3 – 45x 2 5x 2 (2x 2 + 3x – 9 ) 5x (2x – 3)(x + 3 )

You Try:

You Try 30x 3 – 120x 3 0x (x 2 – 4) 3 0x (x – 2)(x + 2)

You Try:

You Try Factor and solve for x-intercepts: x 2 – x + 6 = 0 (x – 3)(x + 2) = 0 (x – 3) = 0 x = 3 (x + 2) = 0 x = -2

Citations :

Citations http://www.purplemath.com/modules/factquad.htm http ://www.mathwarehouse.com/algebra/factor/how-to-factor-trinomials-step-by-step.php

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