Factoring Quadratic Expressions Objectives: Factor a difference of squares. Factor quadratics in the form Factor out the GCF. 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) 4x, 20x 4) x2, 6x 5) 27x2, 36 6) 5x2, 6xy 7) 3y, 8x 8) 2x3, 3x2 9) 36a4, 72a2

Factor out the GCF 1) x2 – 9x 2) 3x2 – 18x

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 4x2 - 25

Perfect Squares 9 is a perfect square because 3 x 3 = 9 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 9x2, 10x2, 81x3, 100x2, 44x2, 1000x4, 30x2

Now you try… Factor: 1) x2 – 4 2) x2 - 81 3) 4x2 – x 4) 25x2 – 9 8) 4x2 + 25 9) 121x2 – 81y2

Factoring Polynomials in the Form ax2 + bx - c 1) x2 – 14x – 32 2) x2 + 13x + 22 3) x2 + 15xy + 14y2 4) x2 + 7x – 12 5) 6x2 + 13x + 2 6) 10x2 – 13x + 4

Factoring Problems with a GCF 1) 4x2 – 16x – 48 2) 6x2 – 42x + 36 3) 2x2 + 46x – 100 4) x3 – 4x 5) 6x2 + 13x + 2 6) 6x2 – 6x - 72