Question

The polynomials ax^3 + 3x^2 - 3 and 2x^3 - 5x^2 + a when divided by (x-4) leaves the remainders M and N respectively. Find the value of a if M+N=0.

Answer 1

M=
$a \times {4}^{3} + 3 \times {4}^{2} - 3 \\ = 64a + 48 - 3 = 64a + 45$
N=
$2 \times {4}^{3} - 5 \times {4}^{2} + a \\ = 128 - 80 + a \\ = 48 + a$
M+N=
$64a + 45 + 48 + a = 0 \\ 65a + 93 = 0 \\ a = \frac{ - 93}{65}$