Question

2x³-3x²-kx-17 divided by x-3 has a reminder of -2
find the value of k ​

Answer 1

k = 4

Explanation:

Polynomials:

p(x) = 2x³ - 3x² - kx - 17

x - 3 = 0

x = 3

It is given that when p(x) is divided by (x - 3), it leaves the remainder -2

⇒ p(3) = -2

2(3)³ - 3(3)² - k *3 - 17 = -2

2*27 -3*9 - 3k -17 = -2

54 - 27 - 3k -17 = -2

-3k + 10 = -2

-3k = -2 - 10

-3k = -12

k = (-12) ÷ (-3)

`\sf \boxed{k = 4}`