How to factor 2x^2+x-1 ?

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

1 Answer
May 10, 2018

2x^2+x-1=color(blue)((x+1)(2x-1)

Explanation:

Factor:

2x^2+x-1

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

Multiply the coefficient of the first term by the constant.

2xx(-1)=-2

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

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

2x^2+2x-x-1

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

2x(x+1)-(x+1) larr -(x+1)=-1(x+1)

Factor out (x+1).

(x+1)(2x-1)