# How do you divide (2x^4+7)/( x^2-1) using polynomial long division?

Mar 11, 2018

$2 {x}^{2}$ +2+ $\frac{9}{{x}^{2} - 1}$

#### Explanation:

1. Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of zero.

2. Divide the highest order term in the dividend $2 {x}^{4}$ by the highest order term in the divisor ${x}^{2}$

3. Multiply the new quotient term by the divisor.

4. The expression needs to be subtracted from the dividend, so change all signs in $2 {x}^{4}$ + 0 - $2 {x}^{2}$

5. After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

6. pull the next terms from the original dividend down into the current dividend.

7. Divide the highest order term in the dividend $2 {x}^{2}$ by the highest order term in the divisor ${x}^{2}$

8. Multiply the new quotient term by the divisor.

9. The expression needs to be subtracted from the dividend, so change all signs in $2 {x}^{2}$ + 0 - 2

10. After changing signs, add the last dividend from the multiplied polynomial to find the new dividend.

11. The final answer is the quotient plus the remainder over the divisor.