Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To match each pair of polynomials with their sum, we need to perform polynomial addition for each pair.
Here are the steps:
1. Sum of First Pair of Polynomials:
- Polynomials: [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex]
Adding these:
[tex]\[ (12x^2 + 3x + 6) + (-7x^2 - 4x - 2) = (12x^2 - 7x^2) + (3x - 4x) + (6 - 2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 5x^2 - x + 4 \][/tex]
2. Sum of Second Pair of Polynomials:
- Polynomials: [tex]\(2x^2 - x\)[/tex] and [tex]\(-2x - 2x^2 - 2\)[/tex]
Adding these:
[tex]\[ (2x^2 - x) + (-2x - 2x^2 - 2) = (2x^2 - 2x^2) + (-x - 2x) + (-2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 0x^2 - 3x - 2 \][/tex]
Which reduces to:
[tex]\[ = -3x - 2 \][/tex]
Note: The only option given without an [tex]\(x^2\)[/tex] term and similar coefficients is [tex]\(-2x - 2\)[/tex]
3. Sum of Third Pair of Polynomials:
- Polynomials: [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex]
Adding these:
[tex]\[ (x + x^2 + 2) + (x^2 - 2 - x) = (x^2 + x^2) + (x - x) + (2 - 2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 2x^2 + 0x + 0 \][/tex]
Which reduces to:
[tex]\[ = 2x^2 \][/tex]
4. Sum of Fourth Pair of Polynomials:
- Polynomials: [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex]
Adding these:
[tex]\[ (x^2 + x) + (x^2 + 8x - 2) = (x^2 + x^2) + (x + 8x) + (-2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 2x^2 + 9x - 2 \][/tex]
Based on the above calculations, we can now match the pairs of polynomials with their sums:
1. [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex] sum to [tex]\(5x^2 - x + 4\)[/tex].
2. [tex]\(2x^2 - x\)[/tex] and [tex]\(-x - 2x^2 - 2\)[/tex] sum to [tex]\(-3x - 2\)[/tex], which matches the given [tex]\(-2x - 2\)[/tex].
3. [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex] sum to [tex]\(2x^2\)[/tex].
4. [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex] sum to [tex]\(2x^2 + 9x - 2\)[/tex].
So, the correct matching pairs are:
- [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex] match with [tex]\(5x^2 - x + 4\)[/tex]
- [tex]\(2x^2 - x\)[/tex] and [tex]\(-x - 2x^2 - 2\)[/tex] match with [tex]\(-2x - 2\)[/tex]
- [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex] match with [tex]\(2x^2\)[/tex]
- [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex] match with [tex]\(2x^2 + 9x - 2\)[/tex]
Here are the steps:
1. Sum of First Pair of Polynomials:
- Polynomials: [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex]
Adding these:
[tex]\[ (12x^2 + 3x + 6) + (-7x^2 - 4x - 2) = (12x^2 - 7x^2) + (3x - 4x) + (6 - 2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 5x^2 - x + 4 \][/tex]
2. Sum of Second Pair of Polynomials:
- Polynomials: [tex]\(2x^2 - x\)[/tex] and [tex]\(-2x - 2x^2 - 2\)[/tex]
Adding these:
[tex]\[ (2x^2 - x) + (-2x - 2x^2 - 2) = (2x^2 - 2x^2) + (-x - 2x) + (-2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 0x^2 - 3x - 2 \][/tex]
Which reduces to:
[tex]\[ = -3x - 2 \][/tex]
Note: The only option given without an [tex]\(x^2\)[/tex] term and similar coefficients is [tex]\(-2x - 2\)[/tex]
3. Sum of Third Pair of Polynomials:
- Polynomials: [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex]
Adding these:
[tex]\[ (x + x^2 + 2) + (x^2 - 2 - x) = (x^2 + x^2) + (x - x) + (2 - 2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 2x^2 + 0x + 0 \][/tex]
Which reduces to:
[tex]\[ = 2x^2 \][/tex]
4. Sum of Fourth Pair of Polynomials:
- Polynomials: [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex]
Adding these:
[tex]\[ (x^2 + x) + (x^2 + 8x - 2) = (x^2 + x^2) + (x + 8x) + (-2) \][/tex]
Simplifying the coefficients separately:
[tex]\[ = 2x^2 + 9x - 2 \][/tex]
Based on the above calculations, we can now match the pairs of polynomials with their sums:
1. [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex] sum to [tex]\(5x^2 - x + 4\)[/tex].
2. [tex]\(2x^2 - x\)[/tex] and [tex]\(-x - 2x^2 - 2\)[/tex] sum to [tex]\(-3x - 2\)[/tex], which matches the given [tex]\(-2x - 2\)[/tex].
3. [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex] sum to [tex]\(2x^2\)[/tex].
4. [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex] sum to [tex]\(2x^2 + 9x - 2\)[/tex].
So, the correct matching pairs are:
- [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex] match with [tex]\(5x^2 - x + 4\)[/tex]
- [tex]\(2x^2 - x\)[/tex] and [tex]\(-x - 2x^2 - 2\)[/tex] match with [tex]\(-2x - 2\)[/tex]
- [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex] match with [tex]\(2x^2\)[/tex]
- [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex] match with [tex]\(2x^2 + 9x - 2\)[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
