# If the polynomial 2x^4+kx^3-11x^2+4x+12  is divided by x-3 the remainder is 60. Find k?

Nov 16, 2016

$k = - 1$

#### Explanation:

By the Remainder Theorem:

$\left\{\begin{matrix}f \left(x\right) \text{ divided by " \\ (x-3)" yields a " \\ "remainder of } 60\end{matrix}\right. \iff f \left(3\right) = 60$

$f \left(x\right) = 2 {x}^{4} + k {x}^{3} - 11 {x}^{2} + 4 x + 12$
$f \left(3\right) = 60 \implies \left(2\right) \left(81\right) + k \left(27\right) - 11 \left(9\right) + 4 \left(3\right) + 12 = 60$
$\therefore 162 + 27 k - 99 + 12 + 12 = 60$
$\therefore 27 k + 87 = 60$
$\therefore 27 k = - 27$
$\therefore k = - 1$