Question 960761: F(x),a 3rd-degree polynomial,G(x) and a 4th-degree polynomial, are both expressions in terms of x.
Does the function H(x)=F(x)[F(x)+G(x)] also need to be a polynomial function in terms of x? If so, what degree is the function H(x)?
A. Yes, it is 21st-degree polynomial in terms of x.
B. Yes, it is a 12th-degree polynomial in terms of x.
C. Yes, it is a 7th-degree polynomial in terms of x.
D. No, it does not need to be a polynomial in terms of x.
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
We use these facts about polynomial sums and products:
#1. The sum of two polynomials is a polynomial with the same degree as the larger of the degrees.
#2. The product of two polynomials is a polynomial with the degree which is the sum of the two degrees of the polynomials.
H(x)=F(x)[F(x)+G(x)]
F(x),a 3rd-degree polynomial,G(x) and a 4th-degree polynomial.
So what we have is:
H(x)=(3rd degree polynomial)[(3rd degree polynomial)+(4th degree polynomial)]
By #1, what's in the bracket is a 4th degree polynomial
H(x)=(3rd degree polynomial)[4th degree polynomial]
By #2, H(x) is a 7th degree polynomial.
Correct answer: C
[It has been proved that in multiple-choice tests, C is the most often
correct answer. So if you ever must guess on such a test, guess C].
Edwin
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