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Section 1.5 : Factoring Polynomials

10. Factor the following polynomial.

\[5{x^2} + 14x - 3\]

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Start Solution

There are only two positive factors of 5 so the initial form for the factoring will be,

\[\left( {5x + \underline {\,\,\,\,\,} } \right)\left( {x + \underline {\,\,\,\,\,} } \right)\]

and the factors of -3 are,

\[\left( { - 1} \right)\left( 3 \right)\,\hspace{0.25in}\left( 1 \right)\left( { - 3} \right)\] Show Step 2

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

\[5{x^2} + 14x - 3 = \require{bbox} \bbox[2pt,border:1px solid black]{{\left( {5x - 1} \right)\left( {x + 3} \right)}}\]