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We have that  3*f(x) + 4*g(x) = h(x) where f(x), g(x) and h(x) are all polynomials in x. If the degree of f(x) is 3 and the degree of h(x) is 5, then what is the minimum possible degree of g(x)?

 Jun 26, 2021
 #1
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Multiplying a polynomial by a constant does not change its degree.   So  3 * f(x) has the same degree as   f(x).

 

   4 * g(x) has the same degree as g(x)         adding 3 (fx) + 4 (g(x)   will not change the degree of the resulting h(x)

             if h(x) is degree 5     then g(x) must be at least degree 5 .

 Jun 26, 2021

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