Question

(8p³ - 38p² - 17p + 43) ÷ (p - 5) 8p² + p - 9, r 9 8p² + p - 5, r 13 8p² + 2p - 7, r 8 8p² + p - 10, r 4

Explanation:

Step1: Divide leading terms

$\frac{8p^3}{p} = 8p^2$

Step2: Multiply divisor by result

$8p^2(p-5) = 8p^3 - 40p^2$

Step3: Subtract from dividend

$(8p^3-38p^2-17p+43)-(8p^3-40p^2) = 2p^2-17p+43$

Step4: Divide new leading terms

$\frac{2p^2}{p} = 2p$

Step5: Multiply divisor by result

$2p(p-5) = 2p^2 - 10p$

Step6: Subtract from new dividend

$(2p^2-17p+43)-(2p^2-10p) = -7p+43$

Step7: Divide leading terms again

$\frac{-7p}{p} = -7$

Step8: Multiply divisor by result

$-7(p-5) = -7p + 35$

Step9: Subtract to find remainder

$(-7p+43)-(-7p+35) = 8$

Step10: Combine quotient terms

$8p^2 + 2p - 7$, remainder 8

Answer:

8p²+2p-7, R 8