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 (that is
b
2
– 4
ac
is a
perfect square) .
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
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 Spring '08
 Staff
 Math, Algebra, Factoring, Factoring Polynomials, Polynomials, Factored Form, GCF

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