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

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Presentation Transcript

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

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

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

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