Answer :
Final answer:
The process for the addition of polynomials is to combine like terms. The terms in the polynomial are added up respectively, forming a new polynomial based on the coefficients and constants. The final result is [tex]10x^6 - 6x^3 + 10x^2 - 6.[/tex]
Explanation:
To answer your question, the first step is to combine like terms. We look at the coefficients of the same degree terms and add or subtract them. Let's start with the x6 terms: 7x6 from the first polynomial added to 3x6 from the second polynomial equals 10x6.
Next, the x2 term from the first polynomial is 10x2. There is no x2 term in the second polynomial, so we leave it as is.
Moving on to the x3 term, there is none in the first polynomial, but in the second there is a -6x3, so it remains -6x3.
Lastly, for the constant term, there is a -10 in the first polynomial and a +4 in the second. Adding these together gives us -6.
So, the final answer is: [tex]10x^6 - 6x^3 + 10x^2 -6.[/tex]
Learn more about Adding Polynomials here:
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