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
8. Factor the following polynomial.
\[{z^2} - 10z + 21\]Show All Steps Hide All Steps
Start SolutionThe initial form for the factoring will be,
\[\left( {z + \underline {\,\,\,\,\,} } \right)\left( {z + \underline {\,\,\,\,\,} } \right)\]and the factors of 21 are,
\[\left( { - 1} \right)\left( { - 21} \right)\,\hspace{0.25in}\left( 1 \right)\left( {21} \right)\hspace{0.25in}\hspace{0.25in}\left( { - 3} \right)\left( { - 7} \right)\hspace{0.25in}\left( 3 \right)\left( 7 \right)\] Show Step 2Now, recalling that we need the pair of factors from the above list that will add to get -10. So, we can see that the correct factoring will then be,
\[{z^2} - 10z + 21 = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {z - 3} \right)\left( {z - 7} \right)}}\]