Math CentralQuandaries & Queries


Question from Jeff, a student:

Factor 10x^2+17x-6 with steps and explanation.

Hi Jeff,

10 can be factored as $10 \times 1$ or $2 \times 5$ and 6 can be factored as $6 \times 1$ or $2 \times 3.$ Let's try factoring 10 as $2 \times 5$ then the possible factorizations of $10x^2 + 17x - 6$ are

\[(5x \pm 3)(2x \pm 2)\]

\[(5x \pm 2)(2x \pm 3)\]

\[(5x \pm 6)(2x \pm 1)\]

\[(5x \pm 1)(2x \pm 6)\]

Since the constant term in the expression $10x^2 + 17x - 6$ is negative you know that the factored form must have opposite signs. Expand the expressions above and see if any gives a middle term of $17x.$ If not then try again with the four possible factorization forms when 10 is factored as $10 \times 1.$

I hope this helps,

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