Question

weeklyquiz - 11 5.6 - 5.7: problem 5
(1 point)
perform the division of polynomials using long division.
\\( \frac { 25 x ^ { 2 } - 10 x - 6 } { 5 x + 2 } = \square + \frac { \square } { \square } \\)
note: you can earn partial credit on this problem.
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Explanation:

Step1: Divide the leading terms

Divide \(25x^{2}\) by \(5x\). \(\frac{25x^{2}}{5x}=5x\)
Multiply \(5x + 2\) by \(5x\): \(5x(5x + 2)=25x^{2}+10x\)
Subtract from \(25x^{2}-10x - 6\): \((25x^{2}-10x - 6)-(25x^{2}+10x)=-20x - 6\)

Step2: Divide the new leading terms

Divide \(-20x\) by \(5x\). \(\frac{-20x}{5x}=-4\)
Multiply \(5x + 2\) by \(-4\): \(-4(5x + 2)=-20x - 8\)
Subtract from \(-20x - 6\): \((-20x - 6)-(-20x - 8)=2\)

Answer:

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