How do you divide #(2x^4+7)/( x^2-1)# using polynomial long division?
1 Answer
Explanation:
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Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of zero.
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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.
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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.
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pull the next terms from the original dividend down into the current dividend.
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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.
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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.
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The final answer is the quotient plus the remainder over the divisor.
