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

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

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Answer 1 · 2018-06-21T14:20:09

$2 (x + 2) (3 x + 1)$ $2(x+2)(3x+1)$

Explanation:

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

first factor out the GCF using the distributive property:

$2 (3 x^{2} + 7 x + 2)$ $2(3x^2+7x+2)$

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

$2 (3 x^{2} + 7 x + 2)$ $2(3x^2+7x+2)$

$2 (3 x^{2} + 6 x + x + 2)$ $2(3x^2+6x+x+2)$

now factor:

$2 (3 x (x + 2) + 1 (x + 2))$ $2(3x(x+2)+1(x+2))$

now factor out the $(x + 2)$ $(x+2)$ :

$2 (x + 2) (3 x + 1)$ $2(x+2)(3x+1)$

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

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Explanation:

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