Started: Jul 10 at 7:13pm
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Question 4
Use synthetic division. Leave your answer in fraction form.
\[
\left(4 x^{5}+23 x^{4}+14 x^{3}+x^{2}+28 x-12\right) \div(x+5)
\]
$4 x^{4}+x^{3}-2 x^{2}+4 x-5-\frac{6}{x+5}$
$4 x^{4}+3 x^{3}-x^{2}+6 x-2-\frac{2}{x+5}$
$4 x^{4}+2 x^{3}+x^{2}-3 x-4-\frac{10}{x+5}$
$4 x^{4}-2 x^{3}+4 x-1-\frac{12}{x+5}$

Answer

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Answer

$\boxed{4x^{4} + 3x^{3} - x^{2} + 6x - 2 - \frac{2}{x+5}}$ is the final result of the synthetic division.

Steps

Step 1 ：The given problem is to perform synthetic division on the polynomial $4x^{5} + 23x^{4} + 14x^{3} + x^{2} + 28x - 12$ by the divisor $x + 5$.

Step 2 ：Synthetic division is a shorthand method of dividing polynomials where we divide the coefficients of the polynomial with the divisor.

Step 3 ：Performing the synthetic division, we get the quotient as $4x^{4} + 3x^{3} - x^{2} + 6x - 2$ and the remainder as $-\frac{2}{x+5}$.

Step 4 ：$\boxed{4x^{4} + 3x^{3} - x^{2} + 6x - 2 - \frac{2}{x+5}}$ is the final result of the synthetic division.