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

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

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Answer 1 · 2015-12-19T22:45:48

Split the middle term then factor by grouping to find:

$2 x^{2} - x - 3 = (2 x - 3) (x + 1)$ $2x^2-x-3 =(2x-3)(x+1)$

Explanation:

Ignoring signs, notice that the coefficient of the middle term is the difference of the two other coefficients. Hence we can split it as follows then factor by grouping:

$2 x^{2} - x - 3$ $2x^2-x-3$

$= 2 x^{2} + 2 x - 3 x - 3$ $= 2x^2+2x-3x-3$

$= (2 x^{2} + 2 x) - (3 x + 3)$ $=(2x^2+2x)-(3x+3)$

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

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

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