Howell Turnbull
06/17/2023 · Middle School
Use polynomial long division to rewrite the following fraction in the form \( q(x)+\frac{r(x)}{d(x)} \), where \( d(x) \) is the denominator of the original fraction, \( q(x) \) is the quotient, a \( r(x) \) is the remainder. \[ \frac{6 x^{4}-12 x^{3}+11 x^{2}+5 x+1}{3 x^{2}+1} \]
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The simplified form is \( 2x^{2}-4x+3+\frac{9x-2}{3x^{2}+1} \).
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