Match each polynomial expression to its additive inverse.
| [tex]$-6 x^2-x-2$[/tex] | | [ ] | [tex]$-6 x^2+x-2$[/tex] |
| [tex]$6 x^2+x-2$[/tex] | | [ ] | [tex]$6 x^2+x+2$[/tex] |
| [tex]$-6 x^2+x-2$[/tex] | | [ ] | [tex]$6 x^2-x+2$[/tex] |
| [tex]$6 x^2-x+2$[/tex] | | [ ] | [tex]$-6 x^2-x+2$[/tex] |
Answer (2)
To find the additive inverses of the given polynomials, we change the signs of each term. The matches are: − 6 x 2 − x − 2 with 6 x 2 + x + 2 , 6 x 2 + x − 2 with − 6 x 2 − x + 2 , and so on. This concept helps in solving equations by isolating variables effectively.
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The additive inverse of a polynomial is found by changing the sign of each term.
− 6 x 2 − x − 2 has an additive inverse of 6 x 2 + x + 2 .
6 x 2 + x − 2 has an additive inverse of − 6 x 2 − x + 2 .
− 6 x 2 + x − 2 has an additive inverse of 6 x 2 − x + 2 .
6 x 2 − x + 2 has an additive inverse of − 6 x 2 + x − 2 .
The final matches are: see explanation .
Explanation
Understanding Additive Inverses We need to find the additive inverse for each given polynomial. The additive inverse is found by changing the sign of each term in the polynomial.
Finding the Inverse of − 6 x 2 − x − 2 For − 6 x 2 − x − 2 , the additive inverse is 6 x 2 + x + 2 .
Finding the Inverse of 6 x 2 + x − 2 For 6 x 2 + x − 2 , the additive inverse is − 6 x 2 − x + 2 .
Finding the Inverse of − 6 x 2 + x − 2 For − 6 x 2 + x − 2 , the additive inverse is 6 x 2 − x + 2 .
Finding the Inverse of 6 x 2 − x + 2 For 6 x 2 − x + 2 , the additive inverse is − 6 x 2 + x − 2 .
Final Matches Therefore, the matches are:
− 6 x 2 − x − 2 matches with 6 x 2 + x + 2
6 x 2 + x − 2 matches with − 6 x 2 − x + 2
− 6 x 2 + x − 2 matches with 6 x 2 − x + 2
6 x 2 − x + 2 matches with $-6x^2 + x - 2
Examples
Additive inverses are useful in many areas of math. For example, when solving equations, we often add the additive inverse to both sides to isolate a variable. If we have the equation x + 5 = 10 , we can add the additive inverse of 5, which is -5, to both sides to get x + 5 + ( − 5 ) = 10 + ( − 5 ) , which simplifies to x = 5 . This concept is also used in physics to represent opposing forces or charges. Understanding additive inverses helps simplify complex problems and find solutions more efficiently.
