Factoring
Polynomials
Greatest Common Factor
1. Check for GCF
2. Find the GCF of all terms
3. Divide each term by GCF
4. The GCF out front
5. Remainder in parentheses
Factor each polynomial
completely.
Factor each polynomial
completely.
Factor each polynomial
completely.
Difference of 2 Squares
a² – b² = (a + b)(a – b)
• Both terms are perfect squares
• The operation is subtraction
• The terms in each binomial are the
square root of the terms in the
problem
• One binomial is addition and one
Factor each polynomial
completely.
Sum / Difference 2
Cubes
a³ – b³ = (a – b)(a² + ab + b²)
a³ + b³ = (a + b)(a² – ab + b²)
• Both terms are perfect cubes
• The operation may be addition or
subtraction
• The terms are a binomial and a
trinomial
• The terms in the binomial are the
cube roots of the terms in the
problem with the same operation
as the problem.
• The 1st term in the trinomial is the
square of the 1st term in the
binomial.
• The 2nd term is the opposite of the
product of the terms in the
binomial.
Factor each polynomial
completely.
Perfect Square
Trinomials
a² + 2ab + b² = (a + b) ²
a² – 2ab + b² = (a – b) ²
• 1st and 3rd terms are perfect
squares
• The middle term is twice the
product of the square roots of the
perfect square terms
Perfect Square Trinomials
• The terms in the binomial are
the square roots of the perfect
square terms in the problem
• The operation is the same as
the middle term
Factor each polynomial
completely.
Factor each polynomial
completely.
Trinomials Reverse FOIL
• Trinomial with a leading coefficient
and / or a constant term that is
prime.
• The first terms of the binomials are
factors of the leading coefficient
and the square roots of the variable
factor.
• List the factors of the constant term
Factor each polynomial completely.
Trinomials Product
Method
1. Multiply the leading coefficient and the
constant term
2. Determine the factors of this product that
add up to the coefficient of the middle
term
3. Split the middle term and factor by
grouping
4. Find the GCF of each binomial
Factor each polynomial
completely.
4 Term Polynomials
1. Look for a perfect square
trinomial
2. Group and factor the perfect
square trinomial
3. Look for a difference of two
squares
4. Factor the difference of two
squares
Factor each polynomial
completely.
Factor by Grouping
1. Grouping can be used with 4
terms
2. Group terms with a common
factor
3. Find the GCF of each binomial
4. Factor out the common term
5. Write polynomial in factored form
Factor each polynomial
completely.