Solving Quadratics By Factoring Worksheet - Chapter 14-1 Page 4
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Section 14–1
Solving Quadratics by Factoring
When the product of two quantities is zero, as in
(x
3)(x
2)
0
we can set each factor equal to zero, getting x
3
0 and
Common
x
2
0.
Error
But this is valid only when the product is zero. Thus if
(x
3)(x
2)
5
we cannot say that x
5 and x
3
2
5.
Often an equation must fi rst be simplifi ed before factoring.
◆◆◆
Example 8:
Solve for x:
x(x
8)
2x(x
1)
9
Solution:
Removing parentheses gives
x
2
8x
2x
2
2x
9
Collecting terms, we get
x
2
6x
9
0
Factoring yields
(x
3)(x
3)
0
which gives the double root,
x
3
◆◆◆
Sometimes at fi rst glance an equation will not look like a quadratic. The following example
shows a fractional equation which, after simplifi cation, turns out to be a quadratic.
Solve for x:
◆◆◆
Example 9:
3x
1
x
1
x
7
4x
7
Solution:
We start by multiplying both sides by the LCD, (4x
7)(x
7). We get
(3x
1)(x
7)
(x
1)(4x
7)
or
2
2
3x
20x
7
4x
11x
7
Collecting terms gives
x
2
9x
14
0
Factoring yields
(x
7)(x
2)
0
so x
7 and x
2.
◆◆◆
Writing the Equation When the Roots Are Known
Given the roots, we simply reverse the process to fi nd the equation.
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