College

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ What is the additive inverse of [tex]$4x^3 - 9x^2 + x - 7$[/tex]?

A. [tex]$-4x^3 + 9x^2 - x - 7$[/tex]
B. [tex]$-4x^3 + 9x^2 + x - 7$[/tex]
C. [tex]$-4x^3 + 9x^2 - x + 7$[/tex]
D. [tex]$-4x^3 - 9x^2 - x - 7$[/tex]

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.