Question

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

Answer 1

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.