Math Problem 4

Define $g(x) = x^3 + 5x^2 -12x -1$. Let $h(x) = 3x^4 + ax^3 - 16x^2 + bx +c$, for $a$, $b$, and $c$ are constants. When $h(x)$ is divided by $g(x)$, the quotient and the remainder are equal.

(a) Find the quotient when $h(x)$ is divided by $g(x)$.

(b) How many rational roots does the equation $h(x) = 0$ have? Show your work.

($3 + 4$ marks)

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