Question

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

Answer 1

`k=-1`

Explanation:

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`