Question

How do you factor `7n ^ { 2} + 45n + 18`?

Answer 1

`(n-6)(n-3/7)`

Explanation:

After dividing by `7` we get
`n^2+45/7n+18/7=0`
using the quadratic Formula

`n_{1,2}=-45/14pm\sqrt(1521/196)`
this is
`n_{1,2}=45/14pm39/14`
so we get
`n_1=6`
`n_2=3/7`
and we get
the product as
`(n-6)(n-3/7)`

Answer 2

`(7n+3)(n+6)`

Explanation:

We can start by factoring by grouping. Here, we will rewrite the `b` term as the sum of two terms. We get

`7n^2+color(blue)(42n+3n)+18`

Notice, what I have in blue is the same as `45n`, so I didn't change the value of the expression.

`color(darkblue)(7n^2+42n)+color(purple)(3n+18)`

I can factor a `7n` out of the dark blue terms, and a `3` out of the purple term. Doing this, we get

`7ncolor(red)((n+6))+3color(red)((n+6))`

Both terms have a `n+6` in common, so we can factor that out. Doing this, we get

`(7n+3)(n+6)`

as our final answer.

Hope this helps!