Solving Quadratics by Factoring
Steps for Solving by Factoring: 1. Make sure all terms are on one side of the equation. 2. Factor. Remember to look for a GCF first! 3. Set each factor equal to 0. 4. Solve.
We can be asked to solve a quadratic equation in lots of ways: -Solve. -Find the x-intercepts. -Find the zeros. -Determine the solutions.
Example 1: Solve: đ?‘Ľ đ?‘Ľ + 3 = 0 This one is already factored, so we can go ahead and set each factor equal to 0: x=0
and
x+3=0
Our solutions will be x = 0 and x = -3.
Example 2: Determine the zeros of đ?‘&#x; ' − 5đ?‘&#x; = 6. First, move the 6 over with the other terms: đ?‘&#x; ' − 5đ?‘&#x; − 6 = 0 Then, factor: đ?‘&#x;−6 đ?‘&#x;+1 =0 Finally, set each factor equal to 0: r–6=0 and r + 1 = 0 r = 6 and r = -1 are the zeros
Example 3: Find the x-intercepts of: 3đ?‘Ľ ' − 4đ?‘Ľ + 1 = 0 All of the terms are already on one side, so it’s time to factor: 3đ?‘Ľ ' − 3đ?‘Ľ − 1đ?‘Ľ + 1 = 0 3đ?‘Ľ đ?‘Ľ − 1 − 1 đ?‘Ľ − 1 = 0 3đ?‘Ľ − 1 đ?‘Ľ − 1 = 0 Then, set each factor to 0 and solve: 3x – 1 = 0 and x – 1 = 0 x = 1/3 and x = 1 are the x-intercepts