5.3 Factoring Quadratics

Factoring : ax2 + bx + c To factor an expression of the form ax2 + bx + c Look for integers r & s such that r · s = a · c and r + s = b. Replace the bx term with rx + sx. Group and factor.

Examples of Factoring : ax2 + bx + c Factor the following: x2 + 7x + 10 mult. to be ac = 10 add to be b = 7 x2 + + 10 (x2 + ) + ( + 10) (x + ) + ( x + ) (x + ) ( x + )

Examples of Factoring : ax2 + bx + c Factor the following: x2 – 3x – 10 mult. to be ac = -10 add to be b = -3 x2 + - 10 (x2 + ) + ( - 10) (x + ) + ( x + ) (x + ) ( x + )

Examples of Factoring : ax2 + bx + c Factor the following: 2x2 + 9x + 10 mult. to be ac = 20 add to be b = 9 2x2 + + 10 (2x2 + ) + ( + 10) ( x + ) + ( x + ) ( x + ) ( x + )

Factoring the Difference of Two Squares Multiply the following: (x + 3) (x – 3) Rule for Factoring Difference of Squares: a2 – b2 = (a + b) ( a – b) Example 1 Factor the following: x2 – 25 Example 2 Factor the following: x4 – 16

Factoring Perfect-Square Trinomials Rules for Factoring Perfect-Square Trinomials: a2 + 2ab + b2 = (a + b)2 a2 – 2ab + b2 = (a – b)2 Example 1: 4x2 – 24x + 36

Zero-Product Property If pq = 0, then p = 0 or q = 0. Example 1: What is the solution to the equation (x + 5)(x + 1) = 0?