Answered

Explore IDNLearn.com's extensive Q&A database and find the answers you need. Ask your questions and get detailed, reliable answers from our community of knowledgeable experts.

Drag the tiles to the boxes to form correct pairs.

Match each pair of polynomials to their sum:

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]

A. [tex]-2x - 2[/tex]
B. [tex]2x^2[/tex]
C. [tex]2x^2 + 9x - 2[/tex]
D. [tex]5x^2 - x + 4[/tex]

Sagot :

GinnyAnsweridn
Let's pair each set of polynomials with their sum.

### Pair 1:
First set of polynomials: [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex].
To find the sum, add the corresponding coefficients of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant term.

[tex]\[ 12x^2 + 3x + 6 + (-7x^2 - 4x - 2) = (12 + -7)x^2 + (3 + -4)x + (6 + -2) \][/tex]
[tex]\[ = 5x^2 - x + 4 \][/tex]

So, the matching sum is [tex]\(5x^2 - x + 4\)[/tex].

### Pair 2:
Second set of polynomials: [tex]\(2x^2 - x\)[/tex] and [tex]\(-x - 2x^2 - 2\)[/tex].
Add the corresponding coefficients of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant term.

[tex]\[ 2x^2 - x + (-x - 2x^2 - 2) = (2 + -2)x^2 + (-1 + -1)x + 0 + -2 \][/tex]
[tex]\[ = 0x^2 - 2x - 2 \][/tex]
[tex]\[ = -2x - 2 \][/tex]

So, the matching sum is [tex]\(-2x - 2\)[/tex].

### Pair 3:
Third set of polynomials: [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex].
Add the corresponding coefficients of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant term.

[tex]\[ x + x^2 + 2 + (x^2 - 2 - x) = (1 + 1)x^2 + (1 + -1)x + (2 + -2) \][/tex]
[tex]\[ = 2x^2 + 0x + 0 \][/tex]
[tex]\[ = 2x^2 \][/tex]

So, the matching sum is [tex]\(2x^2\)[/tex].

### Pair 4:
Fourth set of polynomials: [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex].
Add the corresponding coefficients of [tex]\(x^2\)[/tex], [tex]\(x\)[/tex], and the constant term.

[tex]\[ x^2 + x + (x^2 + 8x - 2) = (1 + 1)x^2 + (1 + 8)x + 0 + -2 \][/tex]
[tex]\[ = 2x^2 + 9x - 2 \][/tex]

So, the matching sum is [tex]\(2x^2 + 9x - 2\)[/tex].

### Summary of Pairs:
- [tex]\(12x^2 + 3x + 6\)[/tex] and [tex]\(-7x^2 - 4x - 2\)[/tex] => [tex]\(5x^2 - x + 4\)[/tex]
- [tex]\(2x^2 - x\)[/tex] and [tex]\(-x - 2x^2 - 2\)[/tex] => [tex]\(-2x - 2\)[/tex]
- [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex] => [tex]\(2x^2\)[/tex]
- [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8x - 2\)[/tex] => [tex]\(2x^2 + 9x - 2\)[/tex]

Thus, the correct pairs are as follows:
- [tex]\(12 x^2 + 3 x + 6\)[/tex] and [tex]\(-7 x^2 - 4 x - 2\)[/tex] => [tex]\(5 x^2 - x + 4\)[/tex]
- [tex]\(2 x^2 - x\)[/tex] and [tex]\(-x - 2 x^2 - 2\)[/tex] => [tex]\(-2 x - 2\)[/tex]
- [tex]\(x + x^2 + 2\)[/tex] and [tex]\(x^2 - 2 - x\)[/tex] => [tex]\(2 x^2\)[/tex]
- [tex]\(x^2 + x\)[/tex] and [tex]\(x^2 + 8 x - 2\)[/tex] => [tex]\(2 x^2 + 9 x - 2\)[/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Find precise solutions at IDNLearn.com. Thank you for trusting us with your queries, and we hope to see you again.