5 3 Solving Quadratic Equations by Factoring WRITE

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5. 3 Solving Quadratic Equations by Factoring WRITE QUADRATIC EQUATIONS IN INTERCEPT FORM. •

5. 3 Solving Quadratic Equations by Factoring WRITE QUADRATIC EQUATIONS IN INTERCEPT FORM. • SOLVE QUADRATIC EQUATIONS BY FACTORING •

Writing Quadratic Equations Standard form of a quadratic equation. y = ax² + bx

Writing Quadratic Equations Standard form of a quadratic equation. y = ax² + bx + c Intercept form of a quadratic equation. y = (x – p)(x – q) Where “p” and “q” are the x-intercepts of the graph. How to write an equation in standard form given x-intercepts. 1. Replace “p” and “q” with the given x-intercepts. 2. Multiply (FOIL) 3. Combine like terms 4. Eliminate any fractions

Examples Write in standard form with given x-intercepts. 1) 4, 1 2) 3, -5

Examples Write in standard form with given x-intercepts. 1) 4, 1 2) 3, -5 3) 1, ½ 4) -2, ⅓

Solving Expressions by Factoring Factors Numbers that are multiplied together to equal the product.

Solving Expressions by Factoring Factors Numbers that are multiplied together to equal the product. When Factoring an expression the goal is to find its factors and write the factors as a multiplication problem. Factoring is the reverse of the distributive property. Therefore, when factoring you are creating parentheses.

Factoring using GCF �

Factoring using GCF �

Factoring using Difference of Squares �

Factoring using Difference of Squares �

Factoring Trinomials �

Factoring Trinomials �

� Factoring Trinomials

� Factoring Trinomials

Factoring Trinomials �

Factoring Trinomials �

Factoring Trinomials with lead coefficient �

Factoring Trinomials with lead coefficient �

Factor each polynomial completely 1) y² - 81 2) x² + x – 30

Factor each polynomial completely 1) y² - 81 2) x² + x – 30 3) x² + 4 x + 3 4) 6 x² - 27 x + 9 x⁵ 5) 4 xy² - 16 x 6) x² - 2 x - 3

Factoring Perfect Cubes x³ - y³ = (x – y)(x² + xy + y²)

Factoring Perfect Cubes x³ - y³ = (x – y)(x² + xy + y²) x³ + y³ = (x + y)(x² - xy + y²) Factor Hint rewrite numbers as a perfect cubes then factor. 1) x³ + 27 2) y³ - 125 3) 8 x³ - y³

Solving quadratic equations by factoring How to Solve Quadratic Equations 1. Graph and find

Solving quadratic equations by factoring How to Solve Quadratic Equations 1. Graph and find the x-intercepts 2. Set equation equal to zero, factor, and use the zero product property. Zero Product Property For any real numbers “a” and “b”, if a • b = 0, then either a = 0 OR b = 0. If (x + 5)(x – 7) = 0, then x + 5 = 0 OR x – 7 = 0 If 2 x(3 x – 5) = 0, then 2 x = 0 OR 3 x – 5 = 0

Solve by factoring �

Solve by factoring �