At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
To determine which pairs of polynomials are additive inverses, we add each pair and check if the result is zero. The polynomials are as follows:
1. [tex]\( x^2 + 3x - 2 \)[/tex] and [tex]\( -x^2 - 3x + 2 \)[/tex]
2. [tex]\( -y^7 - 10 \)[/tex] and [tex]\( -y^7 + 10 \)[/tex]
3. [tex]\( 6z^5 + 6z^5 - 6z^4 \)[/tex] and [tex]\( (-6z^5) + (-6z^5) + 6z^4 \)[/tex]
4. [tex]\( x - 1 \)[/tex] and [tex]\( 1 - x \)[/tex]
5. [tex]\( -5x^2 - 2x - 10 \)[/tex] and [tex]\( 5x^2 - 2x + 10 \)[/tex]
### Pair 1: [tex]\( x^2 + 3x - 2 \)[/tex] and [tex]\( -x^2 - 3x + 2 \)[/tex]
[tex]\[ (x^2 + 3x - 2) + (-x^2 - 3x + 2) = x^2 - x^2 + 3x - 3x - 2 + 2 = 0 \][/tex]
This pair is an additive inverse.
### Pair 2: [tex]\( -y^7 - 10 \)[/tex] and [tex]\( -y^7 + 10 \)[/tex]
[tex]\[ (-y^7 - 10) + (-y^7 + 10) = -y^7 - y^7 - 10 + 10 = -2y^7 \neq 0 \][/tex]
This pair is not an additive inverse.
### Pair 3: [tex]\( 6z^5 + 6z^5 - 6z^4 \)[/tex] and [tex]\( (-6z^5) + (-6z^5) + 6z^4 \)[/tex]
[tex]\[ (6z^5 + 6z^5 - 6z^4) + (-6z^5 - 6z^5 + 6z^4) = 6z^5 - 6z^5 + 6z^5 - 6z^5 - 6z^4 + 6z^4 = 0 \][/tex]
This pair is an additive inverse.
### Pair 4: [tex]\( x - 1 \)[/tex] and [tex]\( 1 - x \)[/tex]
[tex]\[ (x - 1) + (1 - x) = x - x - 1 + 1 = 0 \][/tex]
This pair is an additive inverse.
### Pair 5: [tex]\( -5x^2 - 2x - 10 \)[/tex] and [tex]\( 5x^2 - 2x + 10 \)[/tex]
[tex]\[ (-5x^2 - 2x - 10) + (5x^2 - 2x + 10) = -5x^2 + 5x^2 - 2x - 2x - 10 + 10 = -4x \neq 0 \][/tex]
This pair is not an additive inverse.
### Conclusion
The polynomials that are listed with their correct additive inverse are:
1. [tex]\( x^2 + 3x - 2 \)[/tex] and [tex]\( -x^2 - 3x + 2 \)[/tex]
3. [tex]\( 6z^5 + 6z^5 - 6z^4 \)[/tex] and [tex]\( (-6z^5) + (-6z^5) + 6z^4 \)[/tex]
4. [tex]\( x - 1 \)[/tex] and [tex]\( 1 - x \)[/tex]
1. [tex]\( x^2 + 3x - 2 \)[/tex] and [tex]\( -x^2 - 3x + 2 \)[/tex]
2. [tex]\( -y^7 - 10 \)[/tex] and [tex]\( -y^7 + 10 \)[/tex]
3. [tex]\( 6z^5 + 6z^5 - 6z^4 \)[/tex] and [tex]\( (-6z^5) + (-6z^5) + 6z^4 \)[/tex]
4. [tex]\( x - 1 \)[/tex] and [tex]\( 1 - x \)[/tex]
5. [tex]\( -5x^2 - 2x - 10 \)[/tex] and [tex]\( 5x^2 - 2x + 10 \)[/tex]
### Pair 1: [tex]\( x^2 + 3x - 2 \)[/tex] and [tex]\( -x^2 - 3x + 2 \)[/tex]
[tex]\[ (x^2 + 3x - 2) + (-x^2 - 3x + 2) = x^2 - x^2 + 3x - 3x - 2 + 2 = 0 \][/tex]
This pair is an additive inverse.
### Pair 2: [tex]\( -y^7 - 10 \)[/tex] and [tex]\( -y^7 + 10 \)[/tex]
[tex]\[ (-y^7 - 10) + (-y^7 + 10) = -y^7 - y^7 - 10 + 10 = -2y^7 \neq 0 \][/tex]
This pair is not an additive inverse.
### Pair 3: [tex]\( 6z^5 + 6z^5 - 6z^4 \)[/tex] and [tex]\( (-6z^5) + (-6z^5) + 6z^4 \)[/tex]
[tex]\[ (6z^5 + 6z^5 - 6z^4) + (-6z^5 - 6z^5 + 6z^4) = 6z^5 - 6z^5 + 6z^5 - 6z^5 - 6z^4 + 6z^4 = 0 \][/tex]
This pair is an additive inverse.
### Pair 4: [tex]\( x - 1 \)[/tex] and [tex]\( 1 - x \)[/tex]
[tex]\[ (x - 1) + (1 - x) = x - x - 1 + 1 = 0 \][/tex]
This pair is an additive inverse.
### Pair 5: [tex]\( -5x^2 - 2x - 10 \)[/tex] and [tex]\( 5x^2 - 2x + 10 \)[/tex]
[tex]\[ (-5x^2 - 2x - 10) + (5x^2 - 2x + 10) = -5x^2 + 5x^2 - 2x - 2x - 10 + 10 = -4x \neq 0 \][/tex]
This pair is not an additive inverse.
### Conclusion
The polynomials that are listed with their correct additive inverse are:
1. [tex]\( x^2 + 3x - 2 \)[/tex] and [tex]\( -x^2 - 3x + 2 \)[/tex]
3. [tex]\( 6z^5 + 6z^5 - 6z^4 \)[/tex] and [tex]\( (-6z^5) + (-6z^5) + 6z^4 \)[/tex]
4. [tex]\( x - 1 \)[/tex] and [tex]\( 1 - x \)[/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.