2 Section 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.Standard: N. Solve quadratic equations.
3 I. Factoring Quadratic Expressions To factor an expression containing two or more terms, factor out the greatest common factor (GCF) of the two expressions.Factor each quadratic expression.1. 3a2 – 12a2. 3x(4x + 5) – 5(4x + 5)
8 Example 1 c and dc. x2 + 9x + 20d. x2 – 10x – 11
9 II. Factoring ax2+ bx + c. (Using Trial & Error) To factor an expression of the form ax2+ bx + c where a > 1Find all the factors of cFind all the factors of aPlace the factors of a in the first position of each set of parenthesesPlace the factors of c in the second position of each set of parenthesesTry combinations of factors so that when doing FOIL the Firsts mult to equal a; the Outer and Inners mult then add to equal b; the Lasts mult to equal c
10 Example 2 – Factor and check by graphing Factor 6x2 + 11x Check by graphing.
11 Example 2bFactor 3x2 +11x – 20. Check by graphing.
14 Factoring the Difference of 2 Squares a2 – b2 = (a + b)(a – b)Factor the following expressions:1. y2 - 252. 9x4 - 493. x4 - 16
15 Factoring Perfect Square Trinomials a2 + 2ab + b2 = (a + b)2 or a2 – 2ab + b2 = (a – b)2Factor the following expressions:4x2 – 24x + 36These are called aPerfect Square Trinomial because:9x2 – 36x + 36
16 Zero-Product Property A zero of a function f is any number r such that f(r) = 0.Zero-Product PropertyWhen multiplying two numbers p and q:If p = 0 then p ● q = 0.If q = 0 then p ● q = 0.An equation in the form of ax2+ bx + c = 0 is called the general form of a quadratic equation. The solutions to this equation are called the zeros and are the locations where the parabola crosses the x-axis.