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

Question

Ethan Adkins · Accepted Answer

#2x^2# +2+ #9/( x^2 -1)#

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

Divide the highest order term in the dividend #2x^4# by the highest order term in the divisor #x^2#

Multiply the new quotient term by the divisor.

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

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

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

Divide the highest order term in the dividend #2x^2# by the highest order term in the divisor #x^2#

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all signs in #2x^2# + 0 - 2

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

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

Abigail Allen · Answer

undefined To divide (2x^4+7)/(x^2-1) using polynomial long division, follow these steps:

1. Arrange the terms in descending order of powers of x for both the dividend (2x^4+7) and the divisor (x^2-1).

2. Divide the first term of the dividend (2x^4) by the first term of the divisor (x^2). The result is 2x^2.

3. Multiply the divisor (x^2-1) by the result obtained in step 2 (2x^2). The product is 2x^4-2x^2.

4. Subtract the product obtained in step 3 from the dividend (2x^4+7). This gives (2x^4+7) - (2x^4-2x^2) = 7+2x^2.

5. Bring down the next term from the dividend, which is 0x (since there is no x term in 7+2x^2).

6. Divide the first term of the new dividend (2x^2) by the first term of the divisor (x^2). The result is 2.

7. Multiply the divisor (x^2-1) by the result obtained in step 6 (2). The product is 2x^2-2.

8. Subtract the product obtained in step 7 from the new dividend (2x^2+0x). This gives (2x^2+0x) - (2x^2-2) = 2.

9. Since there are no more terms in the dividend, the division is complete. The quotient is 2x^2+2.

Therefore, (2x^4+7)/(x^2-1) = 2x^2+2.