Download Lesson 2-1 Review of GCF, DOTS and Sum/Product

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Algebra 2: Lesson 2-1 Review of Factoring with GCF, DOTS and Sum/Product
Learning Goals:
1) How do you factor a polynomial using Greatest Common Factor?
2) How do you factor a binomial using Difference of Two Perfect Squares?
3) How do you factor a trinomial using Sum/Product?
4) How do you factor a polynomial completely?
Factoring with Greatest Common Factor (GCF)
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The greatest common factor of two (or more) monomials is the product of the greatest common
factor of the numerical coefficients (the numbers out in front) and the highest power of every
variable that is a factor of each monomial.
When factoring polynomials, look for the largest monomial which is a factor of each term of the
polynomial.
To get the terms within the parentheses, divide each of the original terms by the GCF
Example:
4x3 - 20x2 + 2x
2x(2x2 - 10x + 1)
GCF = 2x
Factoring with Difference of Two Perfect Squares (DOTS)
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An algebraic term is a perfect square when the numerical coefficient (the number in front of the
variables) is a perfect square and the exponents of each of the variables are even numbers.}
The first term in each parenthesis is the square root of the first term of the expression and the
second term in each parenthesis is the square root of the second term of the expression.}
Example:
x2 - 4
(x + 2)(x - 2)
(
)
(
)
Factoring with Sum/Product
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Generally speaking, when the leading coefficient is 1, ask yourself "what numbers multiply to the
last term and add to the middle term?"
The first and last terms are products. The middle term is a sum
{If the last term is positive, the signs are the same.}
ax2 + bx + c
( + )( + )
ax2 - bx + c
( - )( - )
{If the last term is negative, the signs are different.}
ax2 + bx - c
( + )( - )
or
( - )( + )
ax2 - bx - c
( - )( + )
or
( + )( - )
Factoring Completely
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A factorable polynomial with integer coefficients is factored completely when it is written as a
product of unfactorable polynomials with integer coefficients.
When factoring completely, try factoring in this order:
1. Always try GCF first
2. If there are two terms, try DOTS
3. If there are three terms, try Sum/Product
Directions: Factor each completely using the appropriate method(s).
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