# Find the Remainder (9x^4+10x^2-1)÷(x-1/9)

To calculate the remainder, first divide the polynomials.
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
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Divide the highest order term in the dividend by the highest order term in divisor .
 – + + + –
Multiply the new quotient term by the divisor.
 – + + + – + –
The expression needs to be subtracted from the dividend, so change all the signs in
 – + + + – – +
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 by the highest order term in divisor .
 + – + + + – – + + +
Multiply the new quotient term by the divisor.
 + – + + + – – + + + + –
The expression needs to be subtracted from the dividend, so change all the signs in
 + – + + + – – + + + – +
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 by the highest order term in divisor .
 + + – + + + – – + + + – + + +
Multiply the new quotient term by the divisor.
 + + – + + + – – + + + – + + + + –
The expression needs to be subtracted from the dividend, so change all the signs in
 + + – + + + – – + + + – + + + – +
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 by the highest order term in divisor .
 + + + – + + + – – + + + – + + + – + + –
Multiply the new quotient term by the divisor.
 + + + – + + + – – + + + – + + + – + + – + –
The expression needs to be subtracted from the dividend, so change all the signs in
 + + + – + + + – – + + + – + + + – + + – – +
After changing the 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.
Since the last term in the resulting expression is a fraction, the numerator of the fraction is the remainder.
Find the Remainder (9x^4+10x^2-1)÷(x-1/9)

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