Solving Quadratic Equations by Factoring
Procedure — To Solve a Quadratic Equation By Factoring
Step 1 Write the quadratic equation in the form ax2 + bx + c
= 0.
Step 2 Factor the polynomial.
Step 3 Use the Zero Product Property.
Step 4 Solve each equation.
Step 5 Check each answer.
Example
Solve: x2 - 7x + 10 = 0
Solution
| Step 1 Write the quadratic equation in the form ax2
+ bx + c = 0. |
| The equation is given in standard form. |
x2 - 7x + 10 = 0 |
| Step 2 Factor the polynomial.
Find two integers whose product is 10 and
whose sum is -7. They are -5 and -2. |
(x - 5)(x - 2) = 0 |
| Step 3 Use the Zero Product Property.
Set each factor equal to 0. |
x - 5 = 0 or x - 2 = 0 |
| Step 4 Solve each equation. There are two solutions. |
x = 5 or x = 2 |
| Step 5 Check each answer. |
|
| Check x = 5 |
|
Check x = 2 |
|
| Is
Is
Is |
x2 - 7x + 10
(5)2 - 7(5) + 10
25 - 35 + 10
0 |
= 0 = 0 ?
= 0 ?
= 0 ? Yes |
Is
Is
Is |
x2 - 7x + 10
(2)2 - 7(2) + 10
4 - 14 + 10
0 |
= 0 = 0 ?
= 0 ?
= 0 ? Yes |
|
