Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Certainly! Let's analyze and match each pair of polynomials with their corresponding sums.
1. We have four pairs of polynomials to match with the given sums. The pairs of polynomials and the given sums are:
Pairs of polynomials:
1. [tex]\( 12x^2 + 3x + 6 \)[/tex] and [tex]\( -7x^2 - 4x - 2 \)[/tex]
2. [tex]\( 2x^2 - x \)[/tex] and [tex]\( -x - 2x^2 - 2 \)[/tex]
3. [tex]\( x + x^2 + 2 \)[/tex] and [tex]\( x^2 - 2 - x \)[/tex]
4. [tex]\( x^2 + x \)[/tex] and [tex]\( x^2 + 8x - 2 \)[/tex]
Given sums:
1. [tex]\(-2x - 2\)[/tex]
2. [tex]\(2x^2\)[/tex]
3. [tex]\(2x^2 + 9x - 2\)[/tex]
4. [tex]\(5x^2 - x + 4\)[/tex]
2. Let's match each pair of polynomials to their corresponding sum:
Pair 1: [tex]\( 12x^2 + 3x + 6 \)[/tex] and [tex]\( -7x^2 - 4x - 2 \)[/tex]
To find the sum:
[tex]\[ 12x^2 + 3x + 6 + (-7x^2 - 4x - 2) = (12x^2 - 7x^2) + (3x - 4x) + (6 - 2) = 5x^2 - x + 4 \][/tex]
This matches with the sum: [tex]\( 5x^2 - x + 4 \)[/tex]
Pair 2: [tex]\( 2x^2 - x \)[/tex] and [tex]\( -x - 2x^2 - 2 \)[/tex]
To find the sum:
[tex]\[ 2x^2 - x + (-x - 2x^2 - 2) = (2x^2 - 2x^2) + (-x - x) - 2 = -2x - 2 \][/tex]
This matches with the sum: [tex]\( -2x - 2 \)[/tex]
Pair 3: [tex]\( x + x^2 + 2 \)[/tex] and [tex]\( x^2 - 2 - x \)[/tex]
To find the sum:
[tex]\[ x + x^2 + 2 + (x^2 - 2 - x) = (x^2 + x^2) + (x - x) + (2 - 2) = 2x^2 \][/tex]
This matches with the sum: [tex]\( 2x^2 \)[/tex]
Pair 4: [tex]\( x^2 + x \)[/tex] and [tex]\( x^2 + 8x - 2 \)[/tex]
To find the sum:
[tex]\[ x^2 + x + (x^2 + 8x - 2) = (x^2 + x^2) + (x + 8x) - 2 = 2x^2 + 9x - 2 \][/tex]
This matches with the sum: [tex]\( 2x^2 + 9x - 2 \)[/tex]
3. Now, let's summarize the matches:
- Pair [tex]\( (12x^2 + 3x + 6) \)[/tex] and [tex]\( (-7x^2 - 4x - 2) \)[/tex] matches with [tex]\( 5x^2 - x + 4 \)[/tex]
- Pair [tex]\( (2x^2 - x) \)[/tex] and [tex]\( (-x - 2x^2 - 2) \)[/tex] matches with [tex]\( -2x - 2 \)[/tex]
- Pair [tex]\( (x + x^2 + 2) \)[/tex] and [tex]\( (x^2 - 2 - x) \)[/tex] matches with [tex]\( 2x^2 \)[/tex]
- Pair [tex]\( (x^2 + x) \)[/tex] and [tex]\( (x^2 + 8x - 2) \)[/tex] matches with [tex]\( 2x^2 + 9x - 2 \)[/tex]
Thus, the matching of each pair of polynomials to their sum is as follows:
[tex]\[ \begin{align*} 1. & \ (12x^2 + 3x + 6) \ \text{and} \ (-7x^2 - 4x - 2) \to 5x^2 - x + 4 \\ 2. & \ (2x^2 - x) \ \text{and} \ (-x - 2x^2 - 2) \to -2x - 2 \\ 3. & \ (x + x^2 + 2) \ \text{and} \ (x^2 - 2 - x) \to 2x^2 \\ 4. & \ (x^2 + x) \ \text{and} \ (x^2 + 8x - 2) \to 2x^2 + 9x - 2 \\ \end{align*} \][/tex]
1. We have four pairs of polynomials to match with the given sums. The pairs of polynomials and the given sums are:
Pairs of polynomials:
1. [tex]\( 12x^2 + 3x + 6 \)[/tex] and [tex]\( -7x^2 - 4x - 2 \)[/tex]
2. [tex]\( 2x^2 - x \)[/tex] and [tex]\( -x - 2x^2 - 2 \)[/tex]
3. [tex]\( x + x^2 + 2 \)[/tex] and [tex]\( x^2 - 2 - x \)[/tex]
4. [tex]\( x^2 + x \)[/tex] and [tex]\( x^2 + 8x - 2 \)[/tex]
Given sums:
1. [tex]\(-2x - 2\)[/tex]
2. [tex]\(2x^2\)[/tex]
3. [tex]\(2x^2 + 9x - 2\)[/tex]
4. [tex]\(5x^2 - x + 4\)[/tex]
2. Let's match each pair of polynomials to their corresponding sum:
Pair 1: [tex]\( 12x^2 + 3x + 6 \)[/tex] and [tex]\( -7x^2 - 4x - 2 \)[/tex]
To find the sum:
[tex]\[ 12x^2 + 3x + 6 + (-7x^2 - 4x - 2) = (12x^2 - 7x^2) + (3x - 4x) + (6 - 2) = 5x^2 - x + 4 \][/tex]
This matches with the sum: [tex]\( 5x^2 - x + 4 \)[/tex]
Pair 2: [tex]\( 2x^2 - x \)[/tex] and [tex]\( -x - 2x^2 - 2 \)[/tex]
To find the sum:
[tex]\[ 2x^2 - x + (-x - 2x^2 - 2) = (2x^2 - 2x^2) + (-x - x) - 2 = -2x - 2 \][/tex]
This matches with the sum: [tex]\( -2x - 2 \)[/tex]
Pair 3: [tex]\( x + x^2 + 2 \)[/tex] and [tex]\( x^2 - 2 - x \)[/tex]
To find the sum:
[tex]\[ x + x^2 + 2 + (x^2 - 2 - x) = (x^2 + x^2) + (x - x) + (2 - 2) = 2x^2 \][/tex]
This matches with the sum: [tex]\( 2x^2 \)[/tex]
Pair 4: [tex]\( x^2 + x \)[/tex] and [tex]\( x^2 + 8x - 2 \)[/tex]
To find the sum:
[tex]\[ x^2 + x + (x^2 + 8x - 2) = (x^2 + x^2) + (x + 8x) - 2 = 2x^2 + 9x - 2 \][/tex]
This matches with the sum: [tex]\( 2x^2 + 9x - 2 \)[/tex]
3. Now, let's summarize the matches:
- Pair [tex]\( (12x^2 + 3x + 6) \)[/tex] and [tex]\( (-7x^2 - 4x - 2) \)[/tex] matches with [tex]\( 5x^2 - x + 4 \)[/tex]
- Pair [tex]\( (2x^2 - x) \)[/tex] and [tex]\( (-x - 2x^2 - 2) \)[/tex] matches with [tex]\( -2x - 2 \)[/tex]
- Pair [tex]\( (x + x^2 + 2) \)[/tex] and [tex]\( (x^2 - 2 - x) \)[/tex] matches with [tex]\( 2x^2 \)[/tex]
- Pair [tex]\( (x^2 + x) \)[/tex] and [tex]\( (x^2 + 8x - 2) \)[/tex] matches with [tex]\( 2x^2 + 9x - 2 \)[/tex]
Thus, the matching of each pair of polynomials to their sum is as follows:
[tex]\[ \begin{align*} 1. & \ (12x^2 + 3x + 6) \ \text{and} \ (-7x^2 - 4x - 2) \to 5x^2 - x + 4 \\ 2. & \ (2x^2 - x) \ \text{and} \ (-x - 2x^2 - 2) \to -2x - 2 \\ 3. & \ (x + x^2 + 2) \ \text{and} \ (x^2 - 2 - x) \to 2x^2 \\ 4. & \ (x^2 + x) \ \text{and} \ (x^2 + 8x - 2) \to 2x^2 + 9x - 2 \\ \end{align*} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.
