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Solve Polynomial
Equations in
Factored Form
March 25, 2014
Pages 575-579
1. Solve (x – 4)(x + 2) = 0.
(x – 4)(x + 2) = 0
x – 4 = 0 or x + 2 = 0
x = 4 or
x=–2
Write original equation.
Zero-product property
Solve for x.
ANSWER
The solutions of the equation are 4 and –2.
2. Solve the equation (x – 5)(x – 1) = 0.
(x – 5)(x – 1) = 0
x – 5 = 0 or x – 1 = 0
x = 5 or
x=1
Write original equation.
Zero-product property
Solve for x.
ANSWER
The solutions of the equation are 5 and 1.
Factor out the greatest common monomial factor.
3.
12x + 42y
SOLUTION
The GCF of 12 and 42 is 6. The variables x and y
have no common factor. So, the greatest
common monomial factor of the terms is 6.
ANSWER
12x + 42y = 6(2x + 7y)
Factor out the greatest common monomial factor.
4. 4x4 + 24x3
SOLUTION
The GCF of 4 and 24 is 4. The GCF of x4 and x3 is x3.
So, the greatest common monomial factor of the
terms is 4x3.
ANSWER
4x4 + 24x3 = 4x3(x + 6)
5.
Factor out the greatest common monomial factor
from 14m + 35n.
SOLUTION
The GCF of 14 and 35 is 7. The variables m and n have
no common factor. So, the greatest common
monomial factor of the terms is 7.
ANSWER
14m + 35n = 7(2m + 5n)
6. Solve 2x2 + 8x = 0.
2x2 + 8x = 0.
Write original equation.
2x(x + 4) = 0
2x = 0
x=0
Factor left side.
or x + 4 = 0
or
x=–4
Zero-product property
Solve for x.
ANSWER
The solutions of the equation are 0 and – 4.
7. Solve 6n2 = 15n.
6n2 – 15n = 0
Subtract 15n from each side.
3n(2n – 5) = 0
3n = 0
n=0
Factor left side.
or 2n – 5 = 0
or
n=
5
2
Zero-product property
Solve for n.
ANSWER
5
The solutions of the equation are 0 and .
2
Solve the equation.
8. a2 + 5a = 0.
a2 + 5a = 0
Write original equation.
a(a + 5) = 0
Factor left side.
a=0
or a + 5 = 0
a=0
or
a=–5
Zero-product property
Solve for x.
ANSWER
The solutions of the equation are 0 and – 5.
9. 3s2 – 9s = 0.
3s2 – 9s = 0
Write original equation.
3s(s – 3) = 0
3s = 0
s= 0
Factor left side.
or s – 3 = 0
Zero-product property
or
Solve for x.
s=3
ANSWER
The solutions of the equation are 0 and 3.
10.
4x2 = 2x.
4x2 = 2x
Write original equation.
4x2 – 2x = 0
Subtract 2x from each side.
2x(2x – 1) = 0
2x = 0
x=0
Factor left side.
or 2x – 1 = 0
or
x=
1
2
Zero-product property
Solve for x.
ANSWER
1
The solutions of the equation are 0 and .
2
HOMEWORK
Page 578, #4-14, even,
#18-24, even, #28-32, even