Name DateWORKSHEET 5.20: SOLVING QUADRATIC EQUATIONS
BY FACTORING
-------------------------------------------------------------------------------------To solve a quadratic equation by factoring, you must first factor the equation and then use the
zero-product property. The zero-product property states that ifaandbare real numbers and
ab=0, thena=0orb=0. Follow the steps below:- Write the equation so that it is equal to zero (if this is not already done).
- Factor one side of the equation.
- Set each factor equal to zero.
- Solve each equation.
- Substitute your solutions into the original equation to check your work.
EXAMPLE
Solvex^2 + 2 x= 15 by factoring.x^2 + 2 x− 15 = 0
(x−3)(x+5)= 0
(x−3)= 0 or(x+5)= 0
x= 3 or x=− 5
(3)^2 +2(3)= 15 and(−5)^2 +2(−5)= 15DIRECTIONS: Solve each equation by factoring.
- x^2 + 6 x+ 8 = 0 2. 2 x^2 − 8 x+ 6 = 0
- x^2 − 25 = 0 4. x^2 − 10 x+ 24 = 0
- 2 x^2 + 5 x+ 3 = 0 6. 6 x^2 − 14 x=− 8
- x^2 + 9 x=− 14 8. 4 x^2 − 4 x= 24
CHALLENGE:Kim was asked to solvex^2 + 8 x= 7 x+56. She did not know
how to solve it because the equation is not equal to zero. What should she
do to solve this problem?215Copyright
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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.