Solving Quadratic Equations by Factoring
Procedure â€” To Solve a Quadratic Equation By Factoring
Step 1 Write the quadratic equation in the form ax^{2} + 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: x^{2}  7x + 10 = 0
Solution
Step 1 Write the quadratic equation in the form ax^{2}
+ bx + c = 0. 
The equation is given in standard form. 
x^{2}  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 
x^{2}  7x + 10
(5)^{2}  7(5) + 10
25  35 + 10
0 
= 0 = 0 ?
= 0 ?
= 0 ? Yes 
Is
Is
Is 
x^{2}  7x + 10
(2)^{2}  7(2) + 10
4  14 + 10
0 
= 0 = 0 ?
= 0 ?
= 0 ? Yes 
