1. Factor out any common factor .
2.Factor binomials.
3.Factor trinomials.
4.Factor polynomials of more than three terms.
Factoring a Polynomial
Step 1 Factor out any common factor.
Step 2
If the polynomial is a binomial, check to see if it is the difference of
squares , the difference of cubes , or the sum of cubes .
If the polynomial is a trinomial, check to see if it is a perfect square
trinomial . If it is not, factor as in Section 6.2. If the polynomial has more
than three terms , try to factor by grouping .
Step 3Check the factored form by multiplying .
Objective 1
Factor out any common factor.
EXAMPLE 1
Factor each polynomial.
Objective 2
Factor binomials.
Factoring a Binomial
For a binomial ( two terms ), check for the fol lowing :
Difference of Squares:
Difference of Cubes:
Sum of Cubes:
EXAMPLE 2
Factor each binomial, if possible.
Difference of squares
The binomial is prime . It is the sum of squares.
Objective 3
Factor trinomials.
Factoring a Trinomial
For a trinomial (three terms), decide whether it is a
perfect square trinomial of the form
or
If not, use the methods of Section 6.2.
EXAMPLE 3
Factor each trinomial.
Perfect square
trinomial
Two integer factors whose sum is 8(5) = 40 and whose sum
is –13 are –5 and –8.
continued
Factor out the GCF of 3.
Two factors whose product is 2(–21) = –42 and whose sum is
–1 are –7 and 6.
Objective 4
Factor polynomials of more than three terms.
EXAMPLE 4
Factor each polynomial.
continued
