Section 1.5 : Factoring Polynomials
3. Factor out the greatest common factor from the following polynomial.
\[2x{\left( {{x^2} + 1} \right)^3} - 16{\left( {{x^2} + 1} \right)^5}\]Show All Steps Hide All Steps
Start SolutionThe first step is to identify the greatest common factor. In this case it looks like we can factor a 2 and an \({\left( {{x^2} + 1} \right)^3}\) out of each term and so the greatest common factor is \(2{\left( {{x^2} + 1} \right)^3}\) .
Show Step 2Okay, now let’s do the factoring.
\[2x{\left( {{x^2} + 1} \right)^3} - 16{\left( {{x^2} + 1} \right)^5} = \require{bbox} \bbox[2pt,border:1px solid black]{{2{{\left( {{x^2} + 1} \right)}^3}\left( {x - 8{{\left( {{x^2} + 1} \right)}^2}} \right)}}\]Don’t get excited if the greatest common factor has more “complicated” terms in it as this one did. The greatest common factor won’t always be just variables to powers.