Use the remainder theorem!

Algebra Level 2

Given that $x^{ 2 }-5x+4$ is a factor of the expression $2{ x }^{ 4 }+hx^{ 3 }+kx^{ 2 }+34x-24$ . What is the factorized form of the expression?

Hint: Find the values of $h$ and $k$ first.

(x-1)(x-4)(x-3)(3x-2)

(x-1)(x-4)(3x-2)(x+2)

(x-1)(x-4)(2x-3)(3x-2)

(x-1)(x-4)(2x-3)(x+2)