Algebra - Factoring Polynomials

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6. Factor the following polynomial by grouping.

\[18x + 33 - 6{x^4} - 11{x^3}\]

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Start Solution

The first step here is to group the first two term and the last two terms as follows.

\[\left( {18x + 33} \right) - \left( {6{x^4} + 11{x^3}} \right)\]

Be careful with the last grouping. Because both of the terms were negative we needed to factor out an “-” as we did the grouping.

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We can now see that we can factor a 3 out of the first grouping and an \({x^3}\) out of the second grouping. Doing this gives,

\[18x + 33 - 6{x^4} - 11{x^3} = 3\left( {6x + 11} \right) - {x^3}\left( {6x + 11} \right)\] Show Step 3

Finally, we see that we can factor a \(6x + 11\) out of both of the new terms to get,

\[18x + 33 - 6{x^4} - 11{x^3} = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {6x + 11} \right)\left( {3 - {x^3}} \right)}}\]