IDNLearn.com makes it easy to get reliable answers from knowledgeable individuals. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.
Sagot :
To determine which polynomials have the correct additive inverse, we need to check if the sum of the polynomial and its provided inverse equals zero. Let's go through each pair step by step:
1. [tex]\[ x^2 + 3x - 2 \][/tex]
[tex]\[ -x^2 - 3x + 2 \][/tex]
To find the sum:
[tex]\[ (x^2 + 3x - 2) + (-x^2 - 3x + 2) \][/tex]
Combine like terms:
[tex]\[ x^2 - x^2 + 3x - 3x - 2 + 2 = 0 \][/tex]
So, the additive inverse is correct for this pair.
2. [tex]\[ -y^7 - 10 \][/tex]
[tex]\[ -y^7 + 10 \][/tex]
To find the sum:
[tex]\[ (-y^7 - 10) + (-y^7 + 10) \][/tex]
Combine like terms:
[tex]\[ -y^7 - y^7 - 10 + 10 = -2y^7 \][/tex]
This does not simplify to zero. Hence, the additive inverse is incorrect for this pair.
3. [tex]\[ 6z^5 + 6z^5 - 6z^4 \][/tex]
[tex]\[ -6z^5 + (-6z^5) + 6z^4 \][/tex]
To find the sum:
[tex]\[ (6z^5 + 6z^5 - 6z^4) + (-6z^5 + -6z^5 + 6z^4) \][/tex]
Combine like terms:
[tex]\[ 6z^5 - 6z^5 + 6z^5 - 6z^5 - 6z^4 + 6z^4 = 0 \][/tex]
So, the additive inverse is correct for this pair.
4. [tex]\[ x - 1 \][/tex]
[tex]\[ 1 - x \][/tex]
To find the sum:
[tex]\[ (x - 1) + (1 - x) \][/tex]
Combine like terms:
[tex]\[ x - x - 1 + 1 = 0 \][/tex]
So, the additive inverse is correct for this pair.
5. [tex]\[ -5x^2 - 2x - 10 \][/tex]
[tex]\[ 5x^2 - 2x + 10 \][/tex]
To find the sum:
[tex]\[ (-5x^2 - 2x - 10) + (5x^2 - 2x + 10) \][/tex]
Combine like terms:
[tex]\[ -5x^2 + 5x^2 - 2x - 2x - 10 + 10 = -4x \][/tex]
This does not simplify to zero. Hence, the additive inverse is incorrect for this pair.
In summary, the polynomials that are correctly paired with their additive inverse are:
1. [tex]\( x^2 + 3x - 2 \; ; \; -x^2 - 3x + 2 \)[/tex]
3. [tex]\( 6z^5 + 6z^5 - 6z^4 \; ; \; -6z^5 + -6z^5 + 6z^4 \)[/tex]
4. [tex]\( x - 1 \; ; \; 1 - x \)[/tex]
1. [tex]\[ x^2 + 3x - 2 \][/tex]
[tex]\[ -x^2 - 3x + 2 \][/tex]
To find the sum:
[tex]\[ (x^2 + 3x - 2) + (-x^2 - 3x + 2) \][/tex]
Combine like terms:
[tex]\[ x^2 - x^2 + 3x - 3x - 2 + 2 = 0 \][/tex]
So, the additive inverse is correct for this pair.
2. [tex]\[ -y^7 - 10 \][/tex]
[tex]\[ -y^7 + 10 \][/tex]
To find the sum:
[tex]\[ (-y^7 - 10) + (-y^7 + 10) \][/tex]
Combine like terms:
[tex]\[ -y^7 - y^7 - 10 + 10 = -2y^7 \][/tex]
This does not simplify to zero. Hence, the additive inverse is incorrect for this pair.
3. [tex]\[ 6z^5 + 6z^5 - 6z^4 \][/tex]
[tex]\[ -6z^5 + (-6z^5) + 6z^4 \][/tex]
To find the sum:
[tex]\[ (6z^5 + 6z^5 - 6z^4) + (-6z^5 + -6z^5 + 6z^4) \][/tex]
Combine like terms:
[tex]\[ 6z^5 - 6z^5 + 6z^5 - 6z^5 - 6z^4 + 6z^4 = 0 \][/tex]
So, the additive inverse is correct for this pair.
4. [tex]\[ x - 1 \][/tex]
[tex]\[ 1 - x \][/tex]
To find the sum:
[tex]\[ (x - 1) + (1 - x) \][/tex]
Combine like terms:
[tex]\[ x - x - 1 + 1 = 0 \][/tex]
So, the additive inverse is correct for this pair.
5. [tex]\[ -5x^2 - 2x - 10 \][/tex]
[tex]\[ 5x^2 - 2x + 10 \][/tex]
To find the sum:
[tex]\[ (-5x^2 - 2x - 10) + (5x^2 - 2x + 10) \][/tex]
Combine like terms:
[tex]\[ -5x^2 + 5x^2 - 2x - 2x - 10 + 10 = -4x \][/tex]
This does not simplify to zero. Hence, the additive inverse is incorrect for this pair.
In summary, the polynomials that are correctly paired with their additive inverse are:
1. [tex]\( x^2 + 3x - 2 \; ; \; -x^2 - 3x + 2 \)[/tex]
3. [tex]\( 6z^5 + 6z^5 - 6z^4 \; ; \; -6z^5 + -6z^5 + 6z^4 \)[/tex]
4. [tex]\( x - 1 \; ; \; 1 - x \)[/tex]
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.