Math 154 — Rodriguez
Angel — 7.1
Factoring a Monomial from a Polynomial
I. Factoring A Polynomial
A. Definition: A factor is a number that when multiplied by another produces a given
number.
Example: 4⋅3=12 so 4 and 3 are factors of 12.
B. Factoring a polynomial is the process of writing the polynomial as the product of
polynomials.
Have seen: poly as a product = poly as a sum
5x(x + 3) =
Now:
poly as sum = poly as product
4x + 12 = 2(
or
4x + 12 = 4(
THIS IS FACTORING
)
)
C. If a polynomial cannot be factored we say the polynomial is __________.
II. Greatest Common Factor
A. The greatest common factor or GCF is the greatest factor (expression) that evenly
divides each term in the poly.
Example: Determine the GCF of each expression.
1) 5x 6—15x 2
2) 8c2 + 16c—4
3) 12x4— 4x 3 + 8x2
For variables we notice:
B. Factor the GCF from each term in the poly.
Examples:
4) 5x 6—15x 2
5) 8c2 + 16c—4
6) 12x4— 4x 3 + 8x2
C. Factor the negative of the GCF from the poly. (no hw like these)
Example:
7) —4x 3 + 8x2 — 6x
D. Factor the greatest common binomial from the poly. (will see same instructions as
section B above)
Examples:
11)
x(x—5)+3(x—5)
12)
3y(y+2)—4(y+2)
8) x(x—4) + 6(x—4)
9) 4y(2y+5) — 3(2y+5)
10)
Angel — 7.1
3x(x+2)+ x + 2
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