Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Type the correct answer in each box.

Consider these quadratic expressions:

A. [tex]-3x^2 + 11x - 3[/tex]

B. [tex]11x^2 - x + 10[/tex]

C. [tex]4x^2 + 27x - 28[/tex]

D. [tex]-3x^2 + 11x + 31[/tex]

For each polynomial operation, write the letter that corresponds to the resulting expression:

1. [tex](5x^2 + 2x + 1) + (6x^2 - 3x + 9)[/tex] is equivalent to expression [tex]\square[/tex]

2. [tex](-3x^2 + 6x - 12) + 5x + 9[/tex] is equivalent to expression [tex]\square[/tex]

3. [tex](8x + 16) - (3x^2 - 3x - 15)[/tex] is equivalent to expression [tex]\square[/tex]

4. [tex](5x^2 + 23x - 7) - (x^2 - 4x + 21)[/tex] is equivalent to expression [tex]\square[/tex]

Sagot :

GinnyAnswer
Certainly! Let's analyze each polynomial operation step-by-step.

### 1. [tex]\(\left(5x^2 + 2x + 1\right) + \left(6x^2 - 3x + 9\right)\)[/tex]

Combine like terms:

- [tex]\(5x^2 + 6x^2 = 11x^2\)[/tex]
- [tex]\(2x - 3x = -x\)[/tex]
- [tex]\(1 + 9 = 10\)[/tex]

The resulting expression is:
[tex]\[11x^2 - x + 10\][/tex]
This corresponds to expression B.

### 2. [tex]\(\left(-3x^2 + 6x - 12\right) + (5x + 9)\)[/tex]

Combine like terms:

- [tex]\(-3x^2\)[/tex] (no other [tex]\(x^2\)[/tex] term to combine with)
- [tex]\(6x + 5x = 11x\)[/tex]
- [tex]\(-12 + 9 = -3\)[/tex]

The resulting expression is:
[tex]\[-3x^2 + 11x - 3\][/tex]
This corresponds to expression A.

### 3. [tex]\((8x + 16) - \left(3x^2 - 3x - 15\right)\)[/tex]

Distribute the negative sign and combine like terms:

- [tex]\(-3x^2\)[/tex] (no other [tex]\(x^2\)[/tex] term to combine with)
- [tex]\(8x + 3x = 11x\)[/tex]
- [tex]\(16 + 15 = 31\)[/tex]

The resulting expression is:
[tex]\[-3x^2 + 11x + 31\][/tex]
This corresponds to expression D.

### 4. [tex]\(\left(5x^2 + 23x - 7\right) - \left(x^2 - 4x + 21\right)\)[/tex]

Distribute the negative sign and combine like terms:

- [tex]\(5x^2 - x^2 = 4x^2\)[/tex]
- [tex]\(23x + 4x = 27x\)[/tex]
- [tex]\(-7 - 21 = -28\)[/tex]

The resulting expression is:
[tex]\[4x^2 + 27x - 28\][/tex]
This corresponds to expression C.

Summarizing all parts together:

- [tex]\(\left(5x^2 + 2x + 1\right) + \left(6x^2 - 3x + 9\right)\)[/tex] is equivalent to expression B
- [tex]\(\left(-3x^2 + 6x - 12\right) + (5x + 9)\)[/tex] is equivalent to expression A
- [tex]\((8x + 16) - \left(3x^2 - 3x - 15\right)\)[/tex] is equivalent to expression D
- [tex]\(\left(5x^2 + 23x - 7\right) - \left(x^2 - 4x + 21\right)\)[/tex] is equivalent to expression C
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.