Paul's Online Notes
Paul's Online Notes
Home / Algebra / Preliminaries / Factoring Polynomials
Show Mobile Notice Show All Notes Hide All Notes
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 views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 1.5 : Factoring Polynomials

5. Factor the following polynomial by grouping.

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

Show All Steps Hide All Steps

Start Solution

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

\[\left( {7x + 7{x^3}} \right) + \left( {{x^4} + {x^6}} \right)\] Show Step 2

We can now see that we can factor a 7\(x\) out of the first grouping and an \({x^4}\) out of the second grouping. Doing this gives,

\[7x + 7{x^3} + {x^4} + {x^6} = 7x\left( {1 + {x^2}} \right) + {x^4}\left( {1 + {x^2}} \right)\] Show Step 3

Finally, we see that we can factor an \(x\left( {1 + {x^2}} \right)\) out of both of the new terms to get,

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