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SAT Problem of the Day

SAT Problem of the Day. SAT Problem of the Day. 5.3 Factoring Quadratic Expressions. Objectives: Factor a quadratic expression Use factoring to solve a quadratic equation and find the zeros of a quadratic function. Example 1. Factor each quadratic expression. a) 27x 2 – 18x. 27. x 2.

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SAT Problem of the Day

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  1. SAT Problem of the Day

  2. SAT Problem of the Day

  3. 5.3 Factoring Quadratic Expressions Objectives: Factor a quadratic expression Use factoring to solve a quadratic equation and find the zeros of a quadratic function

  4. Example 1 Factor each quadratic expression. a) 27x2 – 18x 27 x2 18 x factor out the GCF for all terms 9 x (3x – 2) b) 5x(2x + 1) – 2(2x + 1) (2x + 1) (2x + 1) factor out the GCF for all terms (2x + 1) ( ) 5x - 2 • Factor a quadratic expression

  5. To factor an expression of the form ax2 + bx + c, where a = 1, look for integers r and s such that r s = c and r + s = b. Then factor the expression. Factoring x2 + bx + c x2 + bx + c = (x + r)(x + s) • Factor a quadratic expression

  6. Example 2 Factor x2 + 12x + 27. ( ) x ( ) x + + 3 9 • Factor a quadratic expression

  7. Example 3 Factor x2 - 15x - 54. ( ) x ( ) x 18 - + 3 • Factor a quadratic expression

  8. Example 4 Factor 5x2 + 14x + 8. ( ) ( ) x 2 + 5x + 4 • Factor a quadratic expression

  9. Practice Factor. 1) 5x2 + 15x 2) (2x – 1)4 + (2x – 1)x 3) x2 + 9x + 20 4) x2 – 7x - 30 5) 3x2 + 11x - 20 • Factor a quadratic expression

  10. Special Products Factoring the Difference of Two Squares a2 – b2 = (a + b)(a – b) Factoring Perfect-Square Trinomials a2 + 2ab + b2 = (a + b)(a + b) a2 - 2ab + b2 = (a - b)(a - b) • Factor a quadratic expression

  11. Example 5 Factor x2 - 16. ( ) ( ) x x 4 - + 4 • Factor a quadratic expression

  12. Example 6 Factor x4 - 81. ( ) ( ) x2 x2 9 - + 9 (x2 + 9) ( ) ( ) x x 3 3 + - • Factor a quadratic expression

  13. Example 7 Factor 2x2 – 24x + 72. 2 24 72 2 ( ) x2 – 12x + 36 2( )( ) x - 6 x - 6 • Factor a quadratic expression

  14. Zero-Product Property If pq = 0, then p = 0 or q = 0. • Find the zeros of a quadratic function

  15. Example 8 Solve . 5x2 + 7x = 0 x(5x + 7) = 0 x = 0 or 5x + 7 = 0 5x = -7 CHECK: CHECK: 5x2 + 7x = 0 5x2 + 7x = 0 5(0)2 + 7(0) = 0 0 + 0 = 0 • Find the zeros of a quadratic function

  16. Example 9 Find the zeroes of the function f(x) = x2 – 5x + 6 x2 – 5x + 6 = 0 (x – 3)(x – 2) = 0 x -3 = 0 or x - 2 = 0 x = 3 x = 2 CHECK: CHECK: x2 – 4x = x - 6 x2 – 4x = x - 6 32 – 4(3) = 3 - 6 22 – 4(2) = 2 - 6 9 – 12 = -3 4 – 8 = -4 -3 = -3 -4 = -4 The zeroes are located at x = 2 and x = 3. • Find the zeros of a quadratic function

  17. Practice Find the zeroes of each function. 1) h(x) = 3x2 + 12x 2) j(x) = x2 + 4x - 21 • Find the zeros of a quadratic function

  18. Collins Type 2 What do you know about the factors of x2+bx+c when c is positive? When c is negative? What information does the sign of b give you in each case? • Factor a quadratic expression

  19. Homework Do the problems listed on page 5 of today's packet ("Finding zeros of quadratic functions using factoring"). Some of these are exercises from Lesson 5.3 of the textbook. • Factor a quadratic expression • Find the zeros of a quadratic function

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