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

9. Factor the following polynomial.

${y^2} + 16y + 60$

Show All Steps Hide All Steps

Start Solution

The initial form for the factoring will be,

$\left( {y + \underline {\,\,\,\,\,} } \right)\left( {y + \underline {\,\,\,\,\,} } \right)$

and the factors of 60 are,

$\begin{array}{c} \left( { - 1} \right)\left( { - 60} \right) & \left( { - 2} \right)\left( { - 30} \right) & \left( { - 3} \right)\left( { - 20} \right) & \left( { - 4} \right)\left( { - 15} \right) & \left( { - 5} \right)\left( { - 12} \right) & \left( { - 6} \right)\left( { - 10} \right)\\ \left( 1 \right)\left( {60} \right) & \left( 2 \right)\left( {30} \right) & \left( 3 \right)\left( {20} \right) & \left( 4 \right)\left( {15} \right) & \left( 5 \right)\left( {12} \right)& \left( 6 \right)\left( {10} \right)\end{array}$

Sometimes there are a lot of factors that we need to deal with. As you get more practice you will start to be able to do most of this in your head and wonâ€™t need to actually write all of the factors down.

Show Step 2

Now, recalling that we need the pair of factors from the above list that will add to get 16. So, we can see that the correct factoring will then be,

${y^2} + 16y + 60 = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {y + 6} \right)\left( {y + 10} \right)}}$