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Answer :
Answer:
3x² +3x +1 +(x -16)/(x⁴ -x³ -7x² +4x +5)
Step-by-step explanation:
You want the result of the division ...
(3x⁶ -23x⁴ -10x³ +20x² +20x -11) ÷ (x⁴ -x³ -7x² +4x +5)
Long division
It works well to write the dividend and divisor in standard form (decreasing exponents) using 0 for the coefficient of missing terms. The long division is carried out in the usual way:
- the quotient term is the ratio of the leading terms
- the next dividend is found by subtracting the product of the quotient term and the divisor from the current dividend.
When the remaining dividend has a degree less than that of the divisor, the process terminates. That remainder can be expressed as a fraction, using the divisor as its denominator.
The details are shown in the attachment. The result is ...
3x² +3x +1 +(x -16)/(x⁴ -x³ -7x² +4x +5)
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