"if the remainder after dividing polynomial (5x^3-3x^2+k) by (x+1) is 4. which o...

Questions

October 2022 1 2 Report

"if the remainder after dividing polynomial (5x^3-3x^2+k) by (x+1) is 4. which of the following must be the value of k?"

with solution po sana pahelp

Answers & Comments

KAntoineDoix

Verified answer

✒️REMAINDER THEOREM

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$\large\underline{\mathbb{PROBLEM}:}$

If the remainder after dividing polynomial (5x³-3x²+k) by (x+1) is 4. which of the following must be the value of k?"

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$\large\underline{\mathbb{ANSWER}:}$

$\qquad \LARGE \:\:\rm{k = 12}$

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$\large\underline{\mathbb{SOLUTION}:}$

» Express the given polynomial as a function P(x). Let (x+1) equate to zero then substitute the value of x to the polynomial function.

$P(x) = 5x^3 - 3x^2 + k \:;\quad x = \text-1$

$P(\text-1) = 5(\text-1)^3 - 3(\text-1)^2 + k$

$P(\text-1) = 5(\text-1) - 3(1) + k$

$P(\text-1) = \text-5 - 3 + k$

$P(\text-1) = \text-8 + k$

» Since dividing P(x) into (x+1) gives a remainder of 4, then P(-1) = 4.

$4 = \text-8 + k$

$4 + 8 = k$

$12 = k$

$\therefore$ The value of k is 12

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