Question

For what value of k is the polynomial 2y³-9y²+y+k is divisible by y-1

Answer 1

$p(y) = 2y {}^{3} - 9y {}^{2} + y + k \\ g(y) = y - 1 \\ by \: factor \: theorem \\ y - 1 = 0 \\ y = 1 \\ so \: remainder \: = p(1) \\ 2 \times 1 {}^{3} - 9 \times 1 {}^{2} + 1 + k = 0 \\ 2 - 9 + 1 + k = 0 \\ 3 - 9 + k = 0 \\ - 6 + k = 0 \\ k = 6$
Hope this will help you