Chapter R - Review of Basic Concepts - R.4 Factoring Polynomials - R.4 Exercises - Page 44: 37

$(3m+2)(m+4)$

Work Step by Step

When factoring $ax^{2}+bx+c$, we search for factors of $ac$ whose sum is $b,$ and, if we find them, we rewrite $bx$ and proceed to factor in groups. Here, factors of $3\times 8=24$ that add to $14$ are $+2$ and $+12.$ $3m^{2}+14m+8=3m^{2}+2m+12m+8$ $=\left(3m^{2}+2m\right)+(12m+8)$ $=m(3m+2)+4(3m+2)$ $=(3m+2)(m+4)$

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