# How do you factor 8v ^ { 2} + 23v - 3 by grouping?

Jun 7, 2017

Break the trinomial into two binomials (8v -1) (1v +3)

#### Explanation:

In the $A {x}^{2} + B x + C$

The C value of -3 indicates that one of the binomials must be positive and one must be negative.

The B value of + 23 indicates that the positive value must be greater than the negative value.

The positive value - the negative value = +23.

Factor 8 and 3 to see possible combinations

8 can be factored into $8 \times 1 : 4 \times 2$
3 can only be factored into $3 \times 1$

$\left(8 \times 3\right) - \left(1 \times 1\right) = 23$ so that is the combination that works.

$8 {v}^{2} + 23 v - 3 = \left(8 v - 1\right) \times \left(1 v + 3\right)$