How do you factor 2x^2+13x-7?

1 Answer
Aug 30, 2016

Find the two binomials whose product is the given trinomial.

2x^2 +13x -7 = ( 2x - 1) xx ( x + 7 )

Explanation:

The -7 shows that one of the binomials must be negative and the other must be positive. If both of the of the binomials were positive the C value would be positive (+7) If both of the binomials were negative the C value would also be positive (+7).

The sum of the negative binomial and the positive binomial will be +13 so the larger product of the binomial must be positive.

2x^2 has only two factors 2 x 1

-7 has only two factors 7 x 1

The larger product will be 2 xx 7 this must be positive.

So, 2x^2 +13x -7 = ( 2x - 1) xx ( x + 7 )

To check, multiply out the brackets. This gives

2x^2 + 14 x - 1 x -7

14x - 1x = 13x larr the middle term is correct.