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Section 1.5 : Factoring Polynomials

7. Factor the following polynomial.

\[{x^2} - 2x - 8\]

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Start Solution

The initial form for the factoring will be,

\[\left( {x + \underline {\,\,\,\,\,} } \right)\left( {x + \underline {\,\,\,\,\,} } \right)\]

and the factors of -8 are,

\[\left( { - 1} \right)\left( 8 \right)\,\hspace{0.25in}\left( 1 \right)\left( { - 8} \right)\hspace{0.25in}\left( { - 2} \right)\left( 4 \right)\hspace{0.25in}\left( 2 \right)\left( { - 4} \right)\] Show Step 2

Now, recalling that we need the pair of factors from the above list that will add to get -2. So, we can see that the correct factoring will then be,

\[{x^2} - 2x - 8 = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {x - 4} \right)\left( {x + 2} \right)}}\]