Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Multiply the polynomials:

[tex](x+3)(3x^2+8x+9)[/tex]

A. [tex]3x^3 + 17x^2 - 15x + 27[/tex]
B. [tex]3x^3 + 17x^2 + 33x - 27[/tex]
C. [tex]3x^3 + x^2 + 33x + 27[/tex]
D. [tex]3x^3 + 17x^2 + 33x + 27[/tex]

Let's multiply the polynomials [tex]\((x + 3)\)[/tex] and [tex]\((3x^2 + 8x + 9)\)[/tex] step-by-step.

1. Distribute the [tex]\(x\)[/tex]:

- Multiply [tex]\(x\)[/tex] by each term in the second polynomial:
- [tex]\(x \times 3x^2 = 3x^3\)[/tex]
- [tex]\(x \times 8x = 8x^2\)[/tex]
- [tex]\(x \times 9 = 9x\)[/tex]

So, the result from the first distribution is:
[tex]\[
3x^3 + 8x^2 + 9x
\][/tex]

2. Distribute the [tex]\(3\)[/tex]:

- Multiply [tex]\(3\)[/tex] by each term in the second polynomial:
- [tex]\(3 \times 3x^2 = 9x^2\)[/tex]
- [tex]\(3 \times 8x = 24x\)[/tex]
- [tex]\(3 \times 9 = 27\)[/tex]

So, the result from this distribution is:
[tex]\[
9x^2 + 24x + 27
\][/tex]

3. Combine the like terms:

Now, add the results from both distributions:
[tex]\[
3x^3 + 8x^2 + 9x + 9x^2 + 24x + 27
\][/tex]

Combine like terms:
- The [tex]\(x^3\)[/tex] term is [tex]\(3x^3\)[/tex].
- Combine the [tex]\(x^2\)[/tex] terms: [tex]\(8x^2 + 9x^2 = 17x^2\)[/tex].
- Combine the [tex]\(x\)[/tex] terms: [tex]\(9x + 24x = 33x\)[/tex].
- The constant term is [tex]\(27\)[/tex].

Therefore, the final polynomial is:
[tex]\[
3x^3 + 17x^2 + 33x + 27
\][/tex]

Thus, the correct answer is:

D. [tex]\(3x^3 + 17x^2 + 33x + 27\)[/tex]