Solving Quadratic Equations By Factoring Worksheet With Answer Key - Tallahassee Community College Page 3
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1
2
3
4
5Example:
Solve: b² + 20 = 9b
First you must put the equation in standard form by subtracting 9b from each side of the
equation.
2
b
20
9
b
+
=
9
b
9
b
−
−
2
b
9
b
20
0
−
+
=
Be sure to put the polynomial in descending order. Be careful to keep the signs with the terms.
b² − 9b + 20 = 0
Now factor the polynomial by finding the factors of 20 that add up to −9.
(b – 4)(b – 5) = 0
Set each factor equal to 0 and solve each equation.
b
4
0
b
5
0
−
=
−
=
4
4
5
5
+
+
+
+
b
4
b
5
=
=
The solutions are 4 and 5.
Example:
Solve: x(x – 11) = 12
In this problem we first have to subtract 12 from each side of the equation. Note that the 12 is
NOT combined with the −11 on the left side of the equation. You cannot combine the two
numbers because the −11 is attached to the x in the parentheses.
x
(
x
11
)
12
−
=
12
12
−
−
x
(
x
11
)
12
0
−
−
=
The equation is now equal to 0, but we need to distribute the x to get the polynomial into
descending order.
x² − 11x – 12 = 0
Now that the equation is in standard form, factor the polynomial.
(x – 12)(x + 1) = 0
Set each factor equal to 0 and solve each equation.
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