Question

find the value of k if the polynomial p(x) = kx³+ 9x²+ 4x- 10 is divided by (x-3) leaves a reminder -22

Answer 1

X=3 remainder therome
P (3)=k (3)3+9 (3)2+4 (3)-10=22
22= 27k+81+12-10
22=27k+83
K=22-83/27
K=61/27

Answer 2

$p(x) = kx {}^{3} + 9x {}^{2} + 4x - 10 \\ g(x) = x - 3 \\ by \: remainder \: theorem \\ x - 3 = 0 \\ x = 3 \\ so \: remainder \: p(3) = - 22 \\ k \times 3 {}^{3} + 9 \times 3 {}^{2} + 4 \times 3 - 10 = - 22 \\ 27k + 81 + 12 - 10 = - 22 \\ 27k = - 22 - 83 \\ 27k = - 105 \\ k = \frac{ - 105}{27}$