Quadratic Equations Worksheet Page 2
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12Solving Quadratic Equations by Factoring
It can also be solved by factoring the equation. Remember to always check your solutions. You can use
direct substitution of the solutions in the equation to see if the solutions satisfy the equation.
−
+ =
2
Examples:
x
5
x
6 0
(
)(
)
← Factoring x
−
−
=
x
3
x
2
0
− =
− =
x
3 0
x
2 0
← Set it equal to 0 and solve for x
=
=
x
3
x
2
−
+ =
2
Now check if, x = 3 and x = 2 are the solutions of x
5
x
6 0
−
+ =
−
+ =
2
2
3
5 3
( )
6 0
2
5 2
( )
6 0
Check:
−
+ =
−
+ =
9 15 6 0
4 10 6 0
+
− =
2
2
x
7
x
4 0
−
+
=
(
2
x
1
)(
x
4
)
0
− =
2
x
1 0
+ =
x
4 0
=
2
x
1
= −
x
4
1
=
x
2
Another method of checking the solutions is by using one of the following
statements:
b
c
−
The sum of the solutions =
or
The product of the solutions =
a
a
+
+ = .
2
where a, b, and c are the coefficients in ax
bx c
0
1
−
+
− =
2
4
are the solutions of 2
x
7
x
4 0
Now we check if x =
and x =
2
1
7
+ −
= −
Check:
Using the sum of the solutions =
(
4
)
2
2
b
7
Based on the original equation = −
= −
a
2
1
−
= −
Now by using the product of the solutions =
(
4
)
2
2
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