# How do you find the quotient of (t^2+5t+4)div(t+4)?

Feb 21, 2017

First, rewrite this expression as:

$\frac{{t}^{2} + 5 t + 4}{t + 4}$

Next, factor the numerator:

$\frac{\left(t + 4\right) \left(t + 1\right)}{t + 4}$

Now, cancel the common terms in the numerator and denominator:

(color(red)(cancel(color(black)((t + 4))))(t + 1))/(color(red)(cancel(color(black)(t + 4)) $= t + 1$ where $t + 4 \ne 0$ or $t \ne - 4$

Feb 21, 2017

You can factorize ${t}^{2} + 5 t + 4 = \left(t + 1\right) \left(t + 4\right)$

#### Explanation:

So now we have:
$= \frac{\left(t + 1\right) \left(t + 4\right)}{t + 4}$

We may now cancel the $\left(t + 4\right)$'s provided $t \ne - 4$

$= \frac{\left(t + 1\right) \cancel{\left(t + 4\right)}}{\cancel{t + 4}} = t + 1$