Question

the polynomial kx^3 + 4x^2 +3x -4 and x^3 -4x +k leave the same remainder when divided by (x -3)find the value of k

Answer 1

$p(x) = kx {}^{3} + 4x {}^{2} + 3x - 4 \\ f(x) = x {}^{3} - 4x + k \\ g(x) = x - 3 \\ by \: factor \: theorem \\ x - 3 = 0 \\ x = 3 \\ so \: remainder \: = p(3) \\if \: both \: leaves \: same \: remainder \: then \\ k \times 3 {}^{3} + 4 \times 3 {}^{2} + 3 \times 3 - 4 = 3 {}^{3} - 4 \times 3 + k \\ 27k + 36 + 9 - 4 = 27 - 12 + k \\ 27k + 41 = 15 + k \\ 27k - k = 15 - 41 \\ 26k = - 26 \\ k = \frac{ - 26}{26} \\ k = - 1$