Question

weeklyquiz - 11 5.6 - 5.7: problem 4
(1 point)
perform the division of polynomials using long division.
\\( \frac { x ^ { 3 } - 8 x ^ { 2 } + 11 x + 8 } { x - 3 } = \square + \frac { \square } { \square } \\)
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Explanation:

Step1: Divide the leading term of the numerator by the leading term of the denominator

Divide \(x^{3}\) by \(x\), we get \(x^{2}\). Then multiply \(x - 3\) by \(x^{2}\) which is \(x^{3}-3x^{2}\). Subtract this from \(x^{3}-8x^{2}+11x + 8\):
\((x^{3}-8x^{2}+11x + 8)-(x^{3}-3x^{2})=-5x^{2}+11x + 8\)

Step2: Repeat the process for the new polynomial

Divide \(-5x^{2}\) by \(x\), we get \(-5x\). Multiply \(x - 3\) by \(-5x\) which is \(-5x^{2}+15x\). Subtract this from \(-5x^{2}+11x + 8\):
\((-5x^{2}+11x + 8)-(-5x^{2}+15x)=-4x + 8\)

Step3: Do it one more time

Divide \(-4x\) by \(x\), we get \(-4\). Multiply \(x - 3\) by \(-4\) which is \(-4x + 12\). Subtract this from \(-4x + 8\):
\((-4x + 8)-(-4x + 12)=-4\)

So \(\frac{x^{3}-8x^{2}+11x + 8}{x - 3}=x^{2}-5x-4+\frac{-4}{x - 3}\)

Answer:

\(x^{2}-5x - 4+\frac{-4}{x - 3}\)