Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
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]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.