Solving Quadratic Equations By Factoring Worksheet With Answer Key - Tallahassee Community College Page 2
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1
2
3
4
52
Example:
Solve: x
+ 6x + 8 = 0
Question to ask: Is the equation in standard form? Yes.
Factor the polynomial by finding the factors of 8 that add up to 6.
2
x
+ 6x + 8 = 0
(x + 4)(x + 2) = 0
Set each factor equal to 0 and solve each equation.
x
4
0
x
2
0
+
=
+
=
4
4
2
2
−
−
−
−
x
4
x
2
=
−
=
−
The solutions are −4 and −2.
2
Example:
Solve: a
– 5a = 24
Question to ask: Is the equation in standard form?
No—the equation is not equal to 0. The first step is to subtract 24 from each side of the equation
so that the equation is equal to 0.
2
a
5
a
24
−
=
24
24
−
−
2
a
5
a
24
0
−
−
=
NOTE: The −24 is placed behind the −5a so that the polynomial is in descending order. Now
factor the polynomial.
a² – 5a – 24 = 0
Find the factors of –24 that add up to –5.
(a – 8)(a + 3) = 0
Set each factor equal to 0 and solve each equation.
a
8
0
a
3
0
−
=
+
=
8
8
3
3
+
+
−
−
a
8
a
3
=
=
−
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