Answer :
To find the additive inverse of a polynomial, you simply change the sign of each term in the polynomial. Let's work through the polynomial [tex]\(4x^3 - 9x^2 + x - 7\)[/tex] together.
1. Start with the polynomial:
[tex]\(4x^3 - 9x^2 + x - 7\)[/tex]
2. Change the sign of each term:
- The term [tex]\(4x^3\)[/tex] becomes [tex]\(-4x^3\)[/tex].
- The term [tex]\(-9x^2\)[/tex] becomes [tex]\(+9x^2\)[/tex].
- The term [tex]\(+x\)[/tex] becomes [tex]\(-x\)[/tex].
- The term [tex]\(-7\)[/tex] becomes [tex]\(+7\)[/tex].
3. Combine the negated terms to get the additive inverse:
[tex]\(-4x^3 + 9x^2 - x + 7\)[/tex]
So, the additive inverse of the polynomial [tex]\(4x^3-9x^2+x-7\)[/tex] is [tex]\(-4x^3 + 9x^2 - x + 7\)[/tex]. Looking at your answer choices, this matches option C.
1. Start with the polynomial:
[tex]\(4x^3 - 9x^2 + x - 7\)[/tex]
2. Change the sign of each term:
- The term [tex]\(4x^3\)[/tex] becomes [tex]\(-4x^3\)[/tex].
- The term [tex]\(-9x^2\)[/tex] becomes [tex]\(+9x^2\)[/tex].
- The term [tex]\(+x\)[/tex] becomes [tex]\(-x\)[/tex].
- The term [tex]\(-7\)[/tex] becomes [tex]\(+7\)[/tex].
3. Combine the negated terms to get the additive inverse:
[tex]\(-4x^3 + 9x^2 - x + 7\)[/tex]
So, the additive inverse of the polynomial [tex]\(4x^3-9x^2+x-7\)[/tex] is [tex]\(-4x^3 + 9x^2 - x + 7\)[/tex]. Looking at your answer choices, this matches option C.
