Math 1300
Section 4.3 Notes
1
Factoring Polynomials
Some trinomials that can be factored do not look like the special trinomials from the
previous sections.
Factor trinomials, written
ax
2
+
bx
+
c
, by doing the following rules:
1.
Factor out the GCF of all three terms.
Use the resulting trinomial for the rest of
the steps.
If
a
is negative, also factor out –1 along with the GCF.
2.
Check that the square root of
b
2
– 4
ac
is a whole number.
If
b
2
– 4
ac
is negative,
then we cannot factor the trinomial.
If the square root of
b
2
– 4
ac
is not a whole
number, then the factored form of
ax
2
+
bx
+
c
will have fractions or square root
signs in it.
We will not be factoring these in this section.
3.
Look at the sign of the constant term.
a.
If the second sign (the one before the constant term) is a + sign, then both signs
in the factored form are whatever the first sign is.
ax
2
+
bx
+
c
= ( __ + __ )( __ + __ )
or
ax
2
–
bx
+
c
= ( __ – __ )( __ – __ )
b.
If the second sign is a – sign, then the signs in the factored form are different.
ax
2
+
bx
–
c
= ( __ + __ )( __ – __ )
or
ax
2
+
bx
–
c
= ( __ + __ )( __ – __ )
4.
Find two numbers that multiply together to give
ac
but add up to give
b
.
Keep the
signs of
a
,
b
, and
c
with the numbers.
5.
Rewrite in preliminary factored form:
a.
Write the GCF on the outside of the factored form.
b.
In both sets of the parentheses, write
ax
c.
Write the appropriate signs from step 3.
d.
Write the two numbers found in step 4, one in each set of parentheses.
6.
Factor out any GCFs from the sets of parentheses and throw them away.
7.
Rewrite.
This is the final factored form.
Examples:
1.
Factor 3
x
2
+ 5
x
+ 4.
Step 1:
Find GCF(3
x
2
, 5
x
, 4).
The GCF is 1 since none of the coefficients have a
factor in common.
Step 2:
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 Spring '08
 Staff
 Math, Factoring, Factoring Polynomials, Polynomials, Addition, GCF

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