This section is a review of the types of factoring we've
covered so far. Follow the steps listed above to factor the
problems.
Example 1
Factor 3x 2 - 27
1 st : Look for a GCF....the GCF is 3 so we factor
out 3: 3( x 2 - 9)
2 nd : Look at the number of terms in the
parenthesis. There are 2 terms and it is the difference of 2
squares. We factor the difference of 2 squares (keeping the 3).
3(x + 3) ( x - 3)
3 rd : Now, make sure the problem is factored
completely. It is.
4 th : Check by multiplying.
Example 2
Factor 9y 2 - 42y + 49
1 st : Look for a GCF....the GCF is 1 so we don't
have to worry about that.
2 nd : Look at the number of terms. There are 3
terms so we factor the trinomial.
-make 2 parentheses
-using the sign rules, we know the signs will be the same
because the constant term is positive
- we also know they will be negative because the
inside/outside combination must equal -58y
-find the factors of the 1 st term: 1y, 9y and 3y, 3y . Let's
try 3y, 3y
-find the factors of the constant term: 1, 49 and 7, 7. Let's
try 7, 7 (3y - 7) (3y - 7)
-check the inside/outside combination: inside we have -21y and
outside we have -21y which adds up to -42y
3 rd : Now, make sure the problem is factored
completely. It is.
4 th : Check by multiplying.
Example 3
Factor x 3 - 5x 2 - 9x + 45
1 st : Look for a GCF....the GCF is 1 so we don't
have to worry about that.
2 nd : Look at the number of terms. There are 4
terms so we factor by grouping.
Group the terms (x 3 - 5x 2 ) + (- 9x +
45 )
Take the GCF of the each group: x 2 (x-
5 )(- 9(x - 5 ))
Take the GCF of the entire problem: (x- 5 )(x
2 -9)
3 rd : Now, make sure the problem is factored
completely. It isn't. We can factor the second parenthesis.
