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How do you factor the expression 6x^2+14x+4?

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Jun 21, 2018

$2 \left(x + 2\right) \left(3 x + 1\right)$

Explanation:

$6 {x}^{2} + 14 x + 4$

first factor out the GCF using the distributive property:

$2 \left(3 {x}^{2} + 7 x + 2\right)$

Factor by grouping, we need a pair of numbers whose sum is $7$ and product is $3 \cdot 2 = 6$ it is immediately clear that $1$ and $6$ will work, so replace the $7 x$ with $6 x + 1 x$

$2 \left(3 {x}^{2} + 7 x + 2\right)$

$2 \left(3 {x}^{2} + 6 x + x + 2\right)$

now factor:

$2 \left(3 x \left(x + 2\right) + 1 \left(x + 2\right)\right)$

now factor out the $\left(x + 2\right)$:

$2 \left(x + 2\right) \left(3 x + 1\right)$

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