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June 19th

June 19th

# The GCF and Factoring by Grouping

Recall, when we multiply one # by another, each # is called a factor.

When we multiply one polynomial by another, each polynomial is also called a factor.
ex. In (x+2) (x-3) =x²-x-6, the factors are (x+2) and (x-3)

To factor a polynomial, we write it as a product.

When factoring a polynomial, we factor out the greatest common factor (GCF).

To find the greatest common factor:
1) Write each coefficient & constant as a product of prime #s (these are factors of the coefficients & constants)
2) The GCF is the product of factors that are common to all the #s

The GCF of the variables is the product of common variables raised to the smallest exponent .

To factor out the GCF, we ‘reverse’ the distributive property . When we find the GCF, we divide it into each term and use those answers to form the other factor.

When a polynomial has 4, 6, 8... terms, we can factor by grouping . To factor by grouping,
1) Arrange the terms so that the 1st 2 have common factors and the last 2 have common factors.
2) Factor out the GCF for each pair of terms
3) Factor out the common binomial
(If the binomial is not common , rearrange the terms & try again)

For any polynomial, if there are no common factors other than 1, the GCF is 1.

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