Question

suppose f(x) = 2x⁴ + 3x³ - kx + 8
if the remainder when f(x) divided by (x - 2) is 44, what is the remainder when f(x) is divided by (x + 1)? (hint:
find k)
type your answer in the boxes

Explanation:

Step1: Apply Remainder Theorem for (x-2)

Remainder = f(2) = 44
$f(2) = 2(2)^4 + 3(2)^3 - k(2) + 8 = 44$
$2(16) + 3(8) - 2k + 8 = 44$
$32 + 24 - 2k + 8 = 44$
$64 - 2k = 44$

Step2: Solve for k

$-2k = 44 - 64$
$-2k = -20$
$k = 10$

Step3: Find remainder when divided by (x+1)

Remainder = f(-1)
$f(-1) = 2(-1)^4 + 3(-1)^3 - 10(-1) + 8$
$= 2(1) + 3(-1) + 10 + 8$
$= 2 - 3 + 10 + 8 = 17$

(Note: Correction—original step 3 calculation error fixed: $2 - 3 + 10 +8 =17$)

Final Answer:

17

Answer:

6