Factoring Polynomials

Factoring Polynomials - Greatest Common Factor(GCF The GCF...

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Greatest Common Factor (GCF) The GCF for a polynomial is the largest monomial that divides (is a factor of) each term of the polynomial. Factoring out the GCF Step 1: Identify the GCF of the polynomial. Step 2: Divide the GCF out of every term of the polynomial. basically the reverse of the distributive property. Example 1 : Factor out the GCF: . View a video of this example Step 1: Identify the GCF of the polynomial.
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The largest monomial that we can factor out of each term is 2 y . Step 2: Divide the GCF out of every term of the polynomial. *Divide 2 y out of every term of the poly. Be careful. If a term of the polynomial is exactly the same as the GCF, when you divide it by the GCF you are left with 1, NOT 0. Don’t think, 'oh I have nothing left', there is actually a 1. As shown above when we divide 2 y by 2 y we get 1, so we need a 1 as the third term inside of the ( ). Note that if we multiply our answer out, we should get the original polynomial. In this case, it does check out. Factoring gives you another way to write the expression so it will be equivalent to the original problem. Example 2 : Factor out the GCF: . View a video of this example This problem looks a little different, because now our GCF is a binomial. That is ok, we treat it in the same manner that we do when we have a monomial GCF. Note that this is not in factored form because of the plus sign we have before the 5 in the problem. To be in factored form, it must be written as a product of factors.
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Step 1: Identify the GCF of the polynomial. This time it isn't a monomial but a binomial that we have in common. Our GCF is (3 x -1). Step 2: Divide the GCF out of every term of the polynomial. *Divide (3 x - 1) out of both parts When we divide out the (3 x - 1) out of the first term, we are left with x . When we divide it out of the second term, we are left with 5. That is how we get the ( x + 5) for our second ( ). Factoring a Polynomial with Four Terms by Grouping In some cases there is not a GCF for ALL the terms in a polynomial. If you have four terms with no GCF, then try factoring by grouping. Step 1: Group the first two terms together and then the last two terms together. Step 2: Factor out a GCF from each separate binomial. Step 3: Factor out the common binomial.
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: Factor by grouping: . View a video of this example Note how there is not a GCF for ALL the terms. So let’s go ahead and factor this by grouping. Step 1: Group the first two terms together and then the last two terms together. *Two groups of two terms Step 2: Factor out a GCF from each separate binomial. *Factor out an x squared from the 1st ( ) *Factor out a 2 from the 2nd ( ) Step 3: Factor out the common binomial. *Divide (
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This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.

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Factoring Polynomials - Greatest Common Factor(GCF The GCF...

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