# A respect for polynomials

Algebra Level 5

Let $$f(x)$$ and $$g(x)$$ be monic cubic polynomials, such that

• $$f(x)+g(x) = p (x)$$,

• $$p(1) = 13$$,

• $$p(3) = 97$$,

• $$p(5) = 349$$,

• $$f(7) = 491$$,

• $$g(19) = 6938$$, and

• $$g(x)$$ is a depressed cubic polynomial.

Evaluate $$f(30) + g (27)$$.

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