Cory writes the polynomial x^7+3x^5+3x+1. Melissa writes the polynomial x^7+5x+10. Is there a difference between the defree of the sum and the degree of the difference of the polynomials?
Answer: Yes, the degree of sum is differ from the degree of difference.
Step-by-step explanation:
Degree of a polynomial is a highest power of its monomials ( single term).
Here, the given polynomials are,
\(x^7+3x^5+3x+1\)
\(x^7+5x+10\)
By adding these two polynomials,
\(x^7+3x^5+3x+1+x^7+5x+10\)
\(=2x^7+3x^5+8x+11\)
Since, the highest power of x in this result = 7
Hence, the degree of sum of the given polynomials = 7
Now, by subtracting the given polynomials,
\((x^7+3x^5+3x+1)-(x^7+5x+10\)
\(=x^7+3x^5+3x+1-x^7-5x-10\)
\(=3x^5-2x-9\)
Since, the highest power of x in this result = 5,
Hence, the degree of difference of the given polynomials = 5
Thus, both the degree of sum and difference are different.
Answer: D- Adding their polynomials together results in a polynomial the degree 7, but subtracting one polynomial from the other results in a polynomial with degree 5.