If $kx^3 + 4x^2 + 3x - 4 $ and $x^3 - 4x + k$ leave the same remainder when divided by (x - 3), then the value of k is:
Answer & explanation
Correct answer: option 2
x - 3 = 0
Then, x = 3
By substituting the value of x, we get
kx3 + 4x2 + 3x - 4
= k(3)3 + 4(3)2 + 3(3) - 4 = 27k + 36 + 9 - 4 = 27k + 41 ----(a)
x3 - 4x + k = 33 - 4(3) + k = 27 - 12 + k = 15 + k ----(b)
Both the dividends leave equal reminders then equating (a) and (b)
27k + 41 = 15 + k
= 26k = -26
= k = -1