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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! smiley

 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

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