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1.Check for GCF2.Find the GCF of all
terms3.Divide each term by
GCF4.The GCF out front5.Remainder in
parentheses
Greatest Common Factor
• 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 binomial is subtraction
Difference of 2 Squares
a² – b² = (a + b)(a – b)
Sum / Difference 2 Cubesa³ – b³ = (a – b)(a² + ab +
b²)
a³ + b³ = (a + b)(a² – ab + b²)
• Both terms are perfect cubes• Operation may be addition or
subtraction• The terms are a binomial and a
trinomial• Rule: Cube root of each term• Rule: Square / Opposite Product /
Square
• 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
a² + 2ab + b² = (a + b) ²
a² – 2ab + b² = (a – b) ²
• 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
Perfect Square Trinomials
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 binomial5. Write the product of your factors
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. Form 2 binomials using the first term in each binomial and the 2 factors in second term in each binomial
4. Divide each binomial by the GCF5. Write the product of your factors
Best Method
4 Term Polynomials1. Look for a perfect square
trinomial2. Group and factor the perfect
square trinomial3. Look for a difference of two
squares4. Factor the difference of two
squares5. Simplify
Factor each polynomial completely.
4 2 24. 9x 12x y 4
2 23. a 8a 16 9b
2 22. y x 9 6x
2 2 21. 4x 25z y 4xy
1. Grouping can be used with 4 terms
2. Group terms with a common factor
3. Find the GCF of each binomial4. Factor out the common term5. Write polynomial in factored
form
Factor by Grouping