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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,
\[{z^2} - 10z + 21 = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {z - 3} \right)\left( {z - 7} \right)}}\]