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# Solving Quadratic Equations by Factoring

Procedure â€” 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
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