How do you factor $8 x^{2} + 14 x + 3$ ?

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Solution

Factor $8 x^{2} + 14 x + 3$ use middle-term splitting.
Split $14$ in two parts such that the sum is $14$ and the product is $24$ as below:
$\begin{array}{rcl} 8 x^{2} + 14 x + 3 & = & 8 x^{2} + 12 x + 2 x + 3 \\ = & (8 x^{2} + 12 x) + (2 x + 3) \\ = & 4 x (2 x + 3) + (2 x + 3) \\ = & (4 x + 1) (2 x + 3) \end{array}$
Hence, the obtained factor form of the given expression is $(4 x + 1) (2 x + 3)$ .

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