Question

algebra 2
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dividing polynomials
divide.

1. $(n^3 - 10n^2 + 26n - 8) \div (n - 4)$

Explanation:

Step1: Use polynomial long division

Divide the leading term of the dividend \(n^3 - 10n^2 + 26n - 8\) by the leading term of the divisor \(n - 4\). The leading term of the dividend is \(n^3\) and the leading term of the divisor is \(n\), so \(n^3\div n = n^2\).
Multiply the divisor \(n - 4\) by \(n^2\) to get \(n^3 - 4n^2\).
Subtract this from the dividend: \((n^3 - 10n^2 + 26n - 8) - (n^3 - 4n^2) = -6n^2 + 26n - 8\).

Step2: Divide the new leading term

The new leading term is \(-6n^2\) and the leading term of the divisor is \(n\), so \(-6n^2\div n = -6n\).
Multiply the divisor \(n - 4\) by \(-6n\) to get \(-6n^2 + 24n\).
Subtract this from the previous result: \((-6n^2 + 26n - 8) - (-6n^2 + 24n) = 2n - 8\).

Step3: Divide the new leading term

The new leading term is \(2n\) and the leading term of the divisor is \(n\), so \(2n\div n = 2\).
Multiply the divisor \(n - 4\) by \(2\) to get \(2n - 8\).
Subtract this from the previous result: \((2n - 8) - (2n - 8) = 0\).

Answer:

\(n^2 - 6n + 2\)