Question

If x³ + 2x² - 6x + 9 is divided by x - 2, then _______ is the remainder.
(a) -13
(b) 13
(c) 9
(d) -16

Answer 1

$x {}^{3} + 2x {}^{2} - 6x + 9 \\ x - 2 = 0 \\ x = 2 \\ p(x) = x {}^{3} + 2x {}^{2} - 6x + 9 \\ p(2) = 2 {}^{3} + 2 \times 2 {}^{2} - 6 \times 2 + 9 \\ 8 + 8 - 12 + 9 \\ 13$
13 is remainder