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Section 1.5 : Factoring Polynomials

1. Factor out the greatest common factor from the following polynomial.

\[6{x^7} + 3{x^4} - 9{x^3}\]

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The first step is to identify the greatest common factor. In this case it looks like we can factor a 3 and an \({x^3}\) out of each term and so the greatest common factor is \(3{x^3}\) .

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Okay, now let’s do the factoring.

\[6{x^7} + 3{x^4} - 9{x^3} = \require{bbox} \bbox[2pt,border:1px solid black]{{3{x^3}\left( {2{x^4} + x - 3} \right)}}\]

Don’t forget to also identify any numbers in the greatest common factor as well. That can often greatly simplify the problem for later work (when we have later work for the problem anyway....).