MATH 0960
5.3 Notes
CHAPTER 5: Factoring
Section 5.3: Factoring Trinomials in the form
Topics:
A. Factor trinomials of the form
, where
B. Remove the greatest common factor from a trinomial.
A. Factor trinomials of the form
 What does a problem look like?
Examples: Factor.
1.
Answer: (
)(
, where
.
.
)
2.
Answer: (

)(
)
What am I supposed to do?
o To factor trinomials in the form
using trial and error
1. Write the polynomial in descending order and factor out the GCF of the
entire polynomial, if any exists.
2. Find all possible pairs of factors of the constant, .
3. Set up each possible pair of factors of the polynomial
in the
form
(
)(
). Filling in the empty spots with pairs of
factors.
4. FOIL to check.
o To factor trinomials in the form
using the c-method
1. Find all pairs of factors whose product equals .
2. Find the pair of factors whose sum equals .
3. Put one of the factors you found in part 2 in each of the blanks
(
)(
).
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MATH 0960
5.3 Notes

What do I need to know?
o Organize your factors; try writing them so the first factor goes from smallest
to largest.
o Some polynomials have 2 variables. These polynomials are in the form
. Factor them as (
)(
).
o If you have tried every possible pair of factors and none of them multiply to
get the original polynomial and none of them work, the polynomial is prime.
o “A prime polynomial is a polynomial that cannot be factored using only
integer coefficients.” -page 298

Examples: Factor each polynomial. If the polynomial is prime, so state.
1.
Answer: Prime
2.
Answer: (
)(
)
B. Remove the greatest common factor from a trinomial.
 What does a problem look like?
Factor completely.
Answer: (
)(
)
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