How do you factor: $2 x^{2} + 7 x + 3$ $2x^2 + 7x +3$ ?

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How do you factor: $2 x^{2} + 7 x + 3$ $2x^2 + 7x +3$ ?

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Answer 1 · 2018-04-10T07:22:41

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

Explanation:

$using the a-c method of factorising$ $"using the a-c method of factorising"$

$the factors of 2 \times 3 = 6$ $"the factors of "2xx3=6$
$which sum to + 7 are + 6 and + 1$ $"which sum to + 7 are + 6 and + 1"$

$split the middle term using these factors$ $"split the middle term using these factors"$

$\Rightarrow 2 x^{2} + 6 x + x + 3 \leftarrow factor by grouping$ $rArr2x^2+6x+x+3larrcolor(blue)"factor by grouping"$

$= 2 x (x + 3) + 1 (x + 3)$ $=color(red)(2x)(x+3)color(red)(+1)(x+3)$

$take out the common factor (x + 3)$ $"take out the common factor "(x+3)$

$= (x + 3) (2 x + 1)$ $=(x+3)(color(red)(2x+1))$

$\Rightarrow 2 x^{2} + 7 x + 3 = (x + 3) (2 x + 1)$ $rArr2x^2+7x+3=(x+3)(2x+1)$

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How do you factor: $2 x^{2} + 7 x + 3$ $2x^2 + 7x +3$ ?

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