Solving Quadratic Equations by Factoring Factor To Solve

Solving Quadratic Equations by Factoring

Factor To Solve a Quadratic Equation Factor to solve 1. Set trinomial = 0 and factor 2. Set both binomials = 0 and solve them each for x

Quadratic Equation Solutions: • You could get two solutions, one solution, or no solutions • The solutions are the x intercepts of the function • Plugging in a 0 for the y (set the equation = 0) gives x intercepts

Zero-Product Property States that if the product of two factors is zero then one (or both) of the factors must be zero. If ab=0, then either a=0, b=0 or both=0

Solve Quadratic Equation x 2 -11 x + 24 = 0 STEPS: Factor and (x-8)(x-3)=0 set=0 Set both x-8=0 or x-3=0 binomials =0 x-8=0 x-3=0 and solve each x=3 x=8 2 Solutions x = 3, 8

When you find the “x” values, you are finding out where the parabola crosses the x-axis when you graph the quadratic equation.

Make sure your quadratic is in standard form set=0 before you start! 2 4 x =7 x+2 Keep x 2 positive 4 x 2 -7 x-2=0 Factor (4 x+1)(x-2)=0 Solve each for x 4 x+1=0 4 x=-1 1 x=- /4 x-2=0 x=2 1 x=- / 4 , 2

2 2 x +3 x-5=0 (2 x+ )(x- )=0 (2 x+5 )(x- 1 )=0 2 x+5=0 2 x=-5 x-1=0 x=1 x = -2. 5 x=1

Sometimes there is just one solution: 2 x -6 x+11=2 -2 -2 2 x -6 x+9 = 0 Perfect sq. tri. (x-3)2=0 x-3=0 x=3

Solve 4 x 2 -18 x=0 (2 x)(2 x-9)=0 2 x=0 2 x-9=0 2 x=9