Question

If two polynomial ax³+4x²+3x-4 and x³+ a leave the same remainder when divided by (x-3), find the value of a

Answer 1

$x - 3 = 0 \\ x = 3$
Inserting this value in the two equations,
$a \times {3}^{3} + 4 \times {3}^{2} + 3 \times 3 - 4 = {3}^{3} - a \\ 27a + 36 - 9 - 4 = 27 - a \\ 27a + 23 = 27 - a \\ 28a = 4 \\ a = \frac{4}{28} = \frac{1}{7}$