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If f(x) = -7x^4 + 3x^3 + x - 5, and g(x) is a polynomial such that the degree of f(x) + g(x) is 1, then what is the degree of g(x)?

 May 27, 2020
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The degree of a polynomial is the degree of its highest degree term.

 

Therefore, the degree of  f(x)  =  -7x4 + 3x3 + x - 5  is  4.

 

For the degree of  f(x) + g(x)  to be 1,  g(x) must have cancelled out the  -7x4  and the  3x3  terms but left the  x  term.

 

So, g(x) must include a  +7x4  term and a  -3x3  term but no other terms larger than x (and, not just a -x term, that would

cancel out all the x-terms and leave a degree of 0).

 

--->   the degree of  g(x)  must be 4.

 May 28, 2020

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