How do you factor the trinomial $2 x^{2} + 5 x - 3$ $2x^2+5x-3$ ?

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How do you factor the trinomial $2 x^{2} + 5 x - 3$ $2x^2+5x-3$ ?

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Answer 1 · 2018-04-28T11:54:31

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

Explanation:

$using the a-c method for factoring quadratics$ $"using the a-c method for factoring quadratics"$

$the factors of the product 2 \times - 3 = - 6$ $"the factors of the product "2xx-3=-6$

$which sum to + 5 are + 6 and - 1$ $"which sum to + 5 are + 6 and - 1"$

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

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

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

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

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

$\Rightarrow 2 x^{2} + 5 x - 3 = (x + 3) (2 x - 1)$ $rArr2x^2+5x-3=(x+3)(2x-1)$

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How do you factor the trinomial $2 x^{2} + 5 x - 3$ $2x^2+5x-3$ ?

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How do you factor the trinomial $2 x^{2} + 5 x - 3$ $2x^2+5x-3$ ?