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$$\text{We have that 3 \cdot f(x) + 4 \cdot g(x) = h(x) where f(x), g(x), and h(x) are all polynomials in x. If the degree of f(x) is 8 and the degree of h(x) is 9, then what is the minimum possible degree of g(x)? }$$

Thanks!

Jul 18, 2019

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Sorry, I am not very experienced in this topic, my answer may be wrong.

Let's pretend that f(x) is  x8. Since f(x) has a degree of 8.

Let's also pretend that h(x) is 3x8 + 4 * g(x). Where it has a degree of 9.

Now, it should be obvious with the deduction that g(x) must also have a degree of 9 to make the h(x) have a degree of 9.

So the minimum possible degree of g(x) should be 9 ??????????

It is 3x8 because in the problem it states: 3 * f(x)

Jul 19, 2019