Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48

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Presentation transcript:

Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48 1) 10 2) 48 3) 7 Find the greatest common factor (GCF) of each set of numbers. 4) 6,14 5) 12,18,30 6) 4,8,15,20

5.3.1 Factoring Quadratic Expressions Objectives: Factor a quadratic expression

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

Factoring x2 + bx + c 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. x2 + bx + c = (x + r)(x + s)

Example 2 Factor x2 + 12x + 27. ( ) x + 3 ( ) x + 9

Example 3 Factor x2 - 15x - 54. ( ) x + 3 ( ) x - 18

Example 4 Factor 5x2 + 14x + 8. ( ) 5x + 4 ( ) x + 2

Practice Factor. 1) 5x2 + 15x 2) (2x – 1)4 + (2x – 1)x 3) x2 + 9x + 20

Homework p.296 #31,35,37,39,41,43,45,49,53,57

Warm-Up 5 minutes Factor. 1) 3x2 - 15x 2) (3x + 7)x + (3x + 7)8

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

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)

Example 1 Factor x2 - 16. ( ) x + 4 ( ) x - 4

Example 2 Factor x4 - 81. ( ) x2 + 9 ( ) x2 - 9 (x2 + 9) ( ) x + 3 ( ) ( ) x2 + 9 ( ) x2 - 9 (x2 + 9) ( ) x + 3 ( ) x - 3

Example 3 Factor 2x2 – 24x + 72. 2 24 72 2 ( ) x2 – 12x + 36 2( )( ) ( ) x2 – 12x + 36 2( )( ) x - 6 x - 6

Zero-Product Property If pq = 0, then p = 0 or q = 0.

Example 4 Solve . 5x2 + 7x = 0 x(5x + 7) = 0 x = 0 or 5x + 7 = 0 CHECK: 5x2 + 7x = 0 CHECK: 5x2 + 7x = 0 5(0)2 + 7(0) = 0 0 + 0 = 0

Example 5 Find the zeroes of the function f(x) = x2 – 5x + 6 or x - 2 = 0 x = 3 x = 2 CHECK: x2 – 4x = x - 6 CHECK: 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.

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

Homework p.296 #59,61,65,67,69,71,75,79,83