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

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

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Answer 1 · 2018-08-04T17:27:03

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

Explanation:

$factor the quadratic using the a-c method$ $"factor the quadratic using the a-c method"$

$the factors of the product 2 \times 2 = 4$ $"the factors of the product "2xx2=4$

$which sum to + 5 are + 4 and + 1$ $"which sum to "+5" are "+4" and "+1$

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

$2 x^{2} + 4 x + x + 2 \leftarrow factor by grouping$ $2x^2+4x+x+2larrcolor(blue)"factor by grouping"$

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

$take out the common factor (x + 2)$ $"take out the "color(blue)"common factor "(x+2)$

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

$2 x^{2} + 5 x + 2 = (x + 2) (2 x + 1)$ $2x^2+5x+2=(x+2)(2x+1)$

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

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