Question

(k³ - 17k + 32) ÷ (k + 5)

Explanation:

Step1: Use polynomial long division

Divide \(k^3 + 0k^2 - 17k + 32\) by \(k + 5\).
First term: \(\frac{k^3}{k}=k^2\). Multiply \(k + 5\) by \(k^2\): \(k^3 + 5k^2\). Subtract from the dividend: \((k^3 + 0k^2 - 17k + 32)-(k^3 + 5k^2)= -5k^2 - 17k\).

Step2: Next term

Divide \(-5k^2\) by \(k\): \(-5k\). Multiply \(k + 5\) by \(-5k\): \(-5k^2 - 25k\). Subtract: \((-5k^2 - 17k)-(-5k^2 - 25k)= 8k + 32\).

Step3: Next term

Divide \(8k\) by \(k\): \(8\). Multiply \(k + 5\) by \(8\): \(8k + 40\). Subtract: \((8k + 32)-(8k + 40)= -8\).

Answer:

The quotient is \(k^2 - 5k + 8\) and the remainder is \(-8\), so \(\frac{k^3 - 17k + 32}{k + 5}=k^2 - 5k + 8-\frac{8}{k + 5}\)