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

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Answer 1 · 2016-11-16T12:24:44

$k = - 1$ $k=-1$

By the Remainder Theorem:

${ (f(x) " divided by "),((x-3)" yields a "), ("remainder of "60):} <=> f(3)=60$

$f(x)=2x^4+kx^3-11x^2+4x+12$
$f(3)=60 => (2)(81)+k(27)-11(9)+4(3)+12=60$
$:. 162+27k-99+12+12=60$
$:. 27k+87=60$
$:. 27k=-27$
$:. k=-1$

If the polynomial 2x^4+kx^3-11x^2+4x+12 2x4+kx3−11x2+4x+122x^4+kx^3-11x^2+4x+12 is divided by x-3x−3x-3 the remainder is 606060. Find kkk?