Factor the following quadratics completely

2r^2 + 5r - 42

Check if splitting the middle term is possible.

List factors of -84

1 * -84

-1 * 84

2 * -42

-2 * 42

3 * -28

-3 * 28

4 * -21

-4 * 21

6 * -14

-6 * 14

7 * -12

-7 * 12 (these digits satisfy the criteria.)

Split the middle term.

2r^2 + 12r - 7r - 42

Factor by grouping.

2r(r + 6) - 7(r + 6)

Rearrange.

(2r - 7)(r + 6)

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b