Question

How do you factor the trinomial `v^2 + 13v + 42`?

Answer 1

`v^2+13x+42 = (v+6)(v+7)`

Explanation:

In general we have:

`(v+a)(v+b) = v^2+(a+b)v+ab`

Note that:

`6+7=13`

`6xx7 = 42`

So (putting `a=6` and `b=7`) we find:

`v^2+13x+42 = (v+6)(v+7)`

Answer 2

`v^2+13v+42=(v+6)*(v+7)`

Explanation:

Although there are many ways to solve this type of problem, we can try some simple inspection first. We know that we are looking for a solution in the form:

`v^2+13v+42=(v+p)*(v+q)`

We can expand the right-hand side to get:

`(v+p)*(v+q)= v^2+(p+q)v+pq`

So, by inspection we know that we need:

`(p+q)=13` and `pq=42`

Let's start by factoring the product, as this will give us all of the possible integer solutions for `p` and `q`

`42 = 2*3*7`

We notice that `2*3=6` and that `6+7 = 13` so we have our solution where

`p=6` and `q=7` resulting in the factorization:

`v^2+13v+42=(v+6)*(v+7)`