Factoring the GCF from Polynomials

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Factoring the GCF from Polynomials
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Review

• Algebraic Factorization is the writing of an
  expression as the product of prime numbers and
  variables with no variables having an exponent
  greater than one.

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Example

• 14x2y 2 ? 7 ? x ? x ? y

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Steps for Factoring the GCF From Polynomials

• Write down the problem.

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Steps for Factoring the GCF From Polynomials

• Write each term on a separate line and then write
  the algebraic factorization of each term.

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Steps for Factoring the GCF From Polynomials

• Pair up all factors that occur in each term and
  circle them.

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Steps for Factoring the GCF From Polynomials

• Multiply what is circled. This is the GCF. When
  writing the answer, put it outside parenthesis.
  The left-overs for each term should be
  multiplied and put inside parenthesis.

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Example

• Step 1
• Step 2

• 3x3 6x2y 15xy2
• 3x3 3 ? x ? x ? x
• 6x2y 2 ? 3 ? x ? x ? y
• 15xy2 3 ? 5 ? x ? y ? y

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Example
Example

• Step 3

Step 3 Step 4
3x3 3 ? x ? x ? x 6x2y 2 ? 3 ? x ? x
? y 15xy2 3 ? 5 ? x ? y ? y 3x (x2 2xy
5y2)
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Examples

• We will do these together on the board.
• 12a2b 90a2b2c
• 32m2n3 8m2n 56m3n2

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Try these yourself.

• 15x2 20xy
• 3x2 15x
• 20abc 15a2c 5ac