# frac{4x^{2} − x − 23}{x-1} Use polynomial long division to perform the indicated division. Write the polynomial in the form p(x) = d(x)q(x) + r(x)

$\frac{4{x}^{2}-x-23}{x-1}$
Use polynomial long division to perform the indicated division.
Write the polynomial in the form $p\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right)$
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Leonard Stokes
Step 1
Consider the division $\frac{4{x}^{2}-x-23}{x-1}$.
Here, the dividend is $4{x}^{2}-x-23$ and the divisor is x-1.
$\left(\frac{4x+3}{x-1}\right)\left(4{x}^{2}-x-23\right)$
$\frac{4{x}^{2}-4x}{3x-23}$
$\frac{3x-3}{-20}$
Step 2
Write the result in the form of $p\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right)$ as follows.
$4{x}^{2}-x-23=\left(x-1\right)\left(4x+3\right)+\left(-20\right)=\left(x-1\right)\left(4x+3\right)=20$
Result:The polynomial in the form of $p\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right)$ is $4{x}^{2}-x-23=\left(x-1\right)\left(4x+3\right)-20$.