1.3 Factoring Polynomials
Monomial Common Factor
1. Find the greatest common factor (GCF) of the coefficients
2. Find the GCF of the variable factors
3. "Factor out" the monomial common factor
4. Possibly, keep factoring!
Binomial Common Factor
1. Identify the binomial common factor
2. Combine the two other terms into a second binomial
3. Bracket them
Factoring by Grouping
1. Group terms that have a common factor
2. Common Monomial Factor each pair of terms
3. Look for a Binomial Common Factor and factor the
polynomial as outlined on the previous slide.
Common Factor
each term has a coefficient and/or
a variable term in common ​
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Grouping
dealing with four terms ​
also a middle step in decomposition ​
Complex trinomial
ax2 + bx + c, when a ≠ 1 ​
both terms are perfect squares (of squares) ​
find two numbers that multiply to (a)(c)
and add to b then break up the middle term
(decomposition) then factor by grouping ​
Simple trinomial
ax2 + bx + c, when a = 1 ​
find two numbers that multiply to
c and add to b
Difference of squares
just two terms separated by a negative sign (difference)! ​
both terms are perfect squares (of squares) ​
take the square root of each term, or use decomposition.
find two numbers that multiply to (a)(c) and add to ZERO
Perfect Square Trinomial ​
ax2 + bx + c, where ax2 and c are perfect squares! ​
b is actually just 2(√ax2 )(√c) ...think of the middle step of FOIL