Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.5 : Factoring Polynomials
6. Factor the following polynomial by grouping.
\[18x + 33 - 6{x^4} - 11{x^3}\]Show All Steps Hide All Steps
Start SolutionThe 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.
Show Step 2We 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 3Finally, we see that we can factor a \(6x + 11\) out of both of the new terms to get,
\[18x + 33 - 6{x^4} - 11{x^3} = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {6x + 11} \right)\left( {3 - {x^3}} \right)}}\]