# How do you divide (7x^4 - 4x^2 – 36x+ 81 )/((x + 9) )?

Jan 3, 2016

$7 {x}^{4} - 4 {x}^{2} - 36 + 81$

$= \left(x + 9\right) \left(7 {x}^{3} - 63 {x}^{2} + 563 x - 5103\right) + 46008$

#### Explanation:

I like to long divide the coefficients, not forgetting to include a $0$ for any missing power of $x$ (in this case ${x}^{3}$)...

Long division of coefficients is similar to long division of numbers.

We find:

$7 {x}^{4} - 4 {x}^{2} - 36 + 81$

$= \left(x + 9\right) \left(7 {x}^{3} - 63 {x}^{2} + 563 x - 5103\right) + 46008$

That is $\left(7 {x}^{4} - 4 {x}^{2} - 36 + 81\right)$ divided by $\left(x + 9\right)$ results in a quotient $\left(7 {x}^{3} - 63 {x}^{2} + 563 x - 5103\right)$ with remainder $46008$.