1. SAT Problem of the Day

3. 5.3 Factoring Quadratic Expressions 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) 27x 2 – 18x 9 factor out the GCF for all terms (3x – 2) 2718x2x2 x x b) 5x(2x + 1) – 2(2x + 1)factor out the GCF for all terms (2x + 1) ( )5x - 2 (2x + 1) Factor a quadratic expression

5. Factoring x 2 + bx + c To factor an expression of the form ax 2 + bx + c, where a = 1, look for integers r and s such that r s = c and r + s = b. Then factor the expression. x 2 + bx + c =(x + r)(x + s) Factor a quadratic expression

6. Example 2 Factor x 2 + 12x + 27. ( ) xx + + 39 Factor a quadratic expression

7. Example 3 Factor x 2 - 15x - 54. ( ) xx + - 3 18 Factor a quadratic expression

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

9. Practice 1) 5x 2 + 15x Factor. 2) (2x – 1)4 + (2x – 1)x 3) x 2 + 9x + 204) x 2 – 7x - 30 5) 3x 2 + 11x - 20 Factor a quadratic expression

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

11. Example 5 Factor x 2 - 16. ( ) x x + - 4 4 Factor a quadratic expression

12. x2x2 Example 6 Factor x 4 - 81. ( ) x2x2 + - 9 9 (x 2 + 9)( ) xx +- 33 Factor a quadratic expression

13. x - 6 Example 7 Factor 2x 2 – 24x + 72.22472 2( ) x 2 – 12x + 36 2( )( )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.5x 2 + 7x = 0 x(5x + 7) = 0 x = 05x + 7 = 0or 5x = -7 CHECK: 5x 2 + 7x = 0 5(0) 2 + 7(0) = 0 0 + 0 = 0 CHECK: 5x 2 + 7x = 0 Find the zeros of a quadratic function

16. Example 9 Find the zeroes of the functionf(x) = x 2 – 5x + 6 x 2 – 5x + 6 = 0 x -3 = 0x - 2 = 0or x = 2 CHECK: x 2 – 4x = x - 6 3 2 – 4(3) = 3 - 6 9 – 12 = -3 CHECK: x 2 – 4x = x - 6 (x – 3)(x – 2) = 0 x = 3 -3 = -3 2 2 – 4(2) = 2 - 6 4 – 8 = -4 -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) = 3x 2 + 12x2) j(x) = x 2 + 4x - 21 Find the zeros of a quadratic function

18. Collins Type 2 What do you know about the factors of x 2 +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. Find the zeros of a quadratic function Factor a quadratic expression