# What is the quotient of b^3 + 4b^2 – 3b + 126 by b+7?

Apr 10, 2016

${b}^{2} - 3 b + 18$

#### Explanation:

Use long division, as used for integers, to find the quotient.

The divisor is $b + 7$.
Look at the first term of the dividend, i.e. ${b}^{3}$.

What should be multiplied to $b$ (of the divisor) to get the first term of the dividend, i.e. ${b}^{3}$?

$b \times {b}^{2} = {b}^{3}$
Therefore, ${b}^{2}$ becomes the first term of the quotient.

Now, ${b}^{2} \times \left(b + 7\right) = {b}^{3} + 7 {b}^{2}$
Write it below the corresponding terms of the dividend and subtract.

We are now left with $- 3 {b}^{2} - 3 b + 126$.

Repeat.