Factoring Quadratic Expressions Objectives n Factor a difference

Factoring Quadratic Expressions Objectives: n Factor a difference of squares. n Factor quadratics in the form n Factor out the GCF. n Factor quadratics with a GCF.

Definitions Greatest Common Factor – the biggest number that will divide all terms evenly. If there are variables, the lower exponent is in the GCF. examples: Find the GCF 1) 9, 12

Class Work Find the GCF: 1) 18, 20 2) 12, 24, 30 3) 4 x, 20 x 4) x 2, 6 x 5) 27 x 2, 36 6) 5 x 2, 6 xy 7) 3 y, 8 x 8) 2 x 3, 3 x 2 9) 36 a 4, 72 a 2

Factor out the GCF 1) x 2 – 9 x 2) 3 x 2 – 18 x 3) 12 x 3 – 18 x 2 4) 2 x 2 + 4 x + 10

Recognizing a Difference of Squares There are ONLY two terms in the problem. It MUST be a minus sign in the middle. BOTH terms are perfect squares This is an example of a difference of squares 4 x 2 - 25

Perfect Squares 9 is a perfect square because 3 x 3 = 9 36 is a perfect square because 6 x 6 = 36 81 is a perfect square because 9 x 9 = 81 12 is NOT a perfect square because there is no number times itself that will give you 12.

Circle the Perfect Squares 16, 36, 20, 121, 144, 60, 50, 4, 225 9 x 2, 10 x 2, 81 x 3, 100 x 2, 44 x 2, 1000 x 4, 30 x 2

Now you try… Factor: 1) x 2 – 4 2) x 2 - 81 3) 4 x 2 – x 4) 25 x 2 – 9 5) 100 x 4 – 49 6) 49 x 2 - 1 8) 4 x 2 + 25 9) 121 x 2 – 81 y 2

Factoring Polynomials in the Form ax 2 + bx - c Factor: 1) x 2 – 14 x – 32 2) x 2 + 13 x + 22 3) x 2 + 15 xy + 14 y 2 4) x 2 + 7 x – 12 5) 6 x 2 + 13 x + 2 6) 10 x 2 – 13 x + 4

Factoring Problems with a GCF 1) 4 x 2 – 16 x – 48 2) 6 x 2 – 42 x + 36 3) 2 x 2 + 46 x – 100 4) x 3 – 4 x 5) 6 x 2 + 13 x + 2 6) 6 x 2 – 6 x - 72