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### Section 1.5 : Factoring Polynomials

11. Factor the following polynomial.

$6{t^2} - 19t - 7$

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There are two sets of positive factors of 6 and so we will have one of the two following possible initial forms for the factoring.

$\left( {2t + \underline {\,\,\,\,\,} } \right)\left( {3t + \underline {\,\,\,\,\,} } \right)\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}\hspace{0.25in}\left( {6t + \underline {\,\,\,\,\,} } \right)\left( {t + \underline {\,\,\,\,\,} } \right)$

and the factors of -7 are,

$\left( { - 1} \right)\left( 7 \right)\,\hspace{0.25in}\left( 1 \right)\left( { - 7} \right)$ Show Step 2

After some trial and error we see that the correct factoring will then be,

$6{t^2} - 19t - 7 = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {2t - 7} \right)\left( {3t + 1} \right)}}$