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Factoring - PowerPoint PPT Presentation

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Factoring

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  1. Factoring Adapted from Walch Education

  2. Key Concepts • The Zero Product Property states that if the product of two factors is 0, then at least one of the factors is 0. • The greatest common factor, or GCF, is the largest factor that two or more terms share. • The value of a for a quadratic expression in the form ax2 + bx+ c is called the leading coefficient, or lead coefficient, because it is the coefficient of the term with the highest power. 5.2.2: Factoring

  3. Key Concepts, continued • The factored form of the expression will be (x + d)(x + e). • A quadratic expression in the form (ax)2 – b2is called a difference of squares. • The difference of squares (ax)2– b2can be written in factored form as (ax + b)(ax – b). • Although the difference of squares is factorable, the sum of squares is prime. 5.2.2: Factoring

  4. Practice • Solve 8x2 – 8 = –x2+ 56 by factoring. 5.2.2: Factoring

  5. Rewrite the equation (all terms on one side) 5.2.2: Factoring

  6. Factor the difference of squares • The expression on the left side can be rewritten in the form (3x)2 – 82. • We can use this form to rewrite the expression as the difference of squares to factor the expression. • (3x + 8)(3x – 8) = 0 5.2.2: Factoring

  7. Use the Zero Product Property to solve • The expression will equal 0 only when one of the factors is equal to 0. • Set each factor equal to 0 and solve. 5.2.2: Factoring

  8. Your Turn… • Solve x2 + 8x = 20 by factoring. 5.2.2: Factoring

  9. Ms. Dambreville Thanks For Watching!