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 When factoring, identify and factor out the greatest common monomial if, one exists.  The greatest common monomial consists of a number part and/or variable part that is common in each term. 1 st Identify the greatest common monomial.  The polynomial that remains may or may not be factorable. 2 nd If possible, factor the remaining polynomial. 3 rd Check your solution by multiplying the factors together.

3x + 9x – 15x * Factor out the greatest common monomial * 1 st Place polynomial in standard form. * 2 nd Identify prime factorization of each term.   

   Factor: 9x + 3x – 15x * 3 rd Identify the GCF * 4 th Factor out the GCF * 5 th Check by distributing

4 2 8x + 4x – 16x * Factor out the greatest common monomial. * 1 st Place polynomial in standard form. * 2 nd Identify GCF GCF * 3 rd Factor out GCF * 4 th Check 8x 4 4x+ 2 16x –

2 4x – 6 + 2x Sometimes when you factor, you need to factor out the GCF and then factor the remaining polynomial. * 1 st Place polynomial in standard form * 2 nd Identify GCF * 3 rd Factor out GCF

2 ( x + 2x – 3) ( ) 2(x + 3)( x – 1) 1 – 3 x + * 4 th Factor remaining trinomial into product of two binomials. * 5 th Check it Final Answer: x 2(x + 3)( x – 1) Multiply binomial and binomial together

– 4 20x – 4x * 1 st Place polynomial in standard form 2 nd Identify GCF (If the leading coefficient is negative, factor a negative out as part of your GCF) GCF * 3 rd Factor out GCF * 4 th Factor trinomial + x x ( ) 1 – 6 Final Answer: – 4(x + 1)( x – 6)

1 st Look for greatest common monomial. 2 nd Try and factor the remaining polynomial. 3 rd Check your solution by multiplying all factors together.