How to factor $2 x^{2} + x - 1$ $2x^2+x-1$ ?

Question

i tried to factor it and i got $(2 x + 1) (x - 1)$ $(2x+1)(x-1)$
but my friend said the correct answer is $(2 x - 1) (x + 1)$ $(2x-1)(x+1)$

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Answer 1 · 2018-05-10T01:27:31

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

Factor:

$2 x^{2} + x - 1$ $2x^2+x-1$

The method to use is called "splitting the middle term."

Multiply the coefficient of the first term by the constant.

$2 \times (- 1) = - 2$ $2xx(-1)=-2$

Find two number that when added equal $1$ $1$ and when multiplied equal $- 2$ $-2$ . The numbers that meet the criteria are $2$ $2$ and $- 1$ $-1$ .

Rewrite the expression, splitting the middle term $x$ $x$ into $2 x$ $2x$ and $- x$ $-x$ .

$2 x^{2} + 2 x - x - 1$ $2x^2+2x-x-1$

Factor out the common terms in the first two terms and the second two terms.

$2 x (x + 1) - (x + 1)$ $2x(x+1)-(x+1)$ $\leftarrow$ $larr$ $- (x + 1) = - 1 (x + 1)$ $-(x+1)=-1(x+1)$

Factor out $(x + 1)$ $(x+1)$ .

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