College

Multiply the polynomials:

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

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

Answer :

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] in [tex]\((x+3)\)[/tex] to each term in [tex]\((3x^2 + 8x + 9)\)[/tex]:
- [tex]\(x \times 3x^2 = 3x^3\)[/tex]
- [tex]\(x \times 8x = 8x^2\)[/tex]
- [tex]\(x \times 9 = 9x\)[/tex]

So after multiplying with [tex]\(x\)[/tex], we have:
[tex]\[
3x^3 + 8x^2 + 9x
\][/tex]

2. Distribute the [tex]\(3\)[/tex] in [tex]\((x+3)\)[/tex] to each term in [tex]\((3x^2 + 8x + 9)\)[/tex]:
- [tex]\(3 \times 3x^2 = 9x^2\)[/tex]
- [tex]\(3 \times 8x = 24x\)[/tex]
- [tex]\(3 \times 9 = 27\)[/tex]

So after multiplying with [tex]\(3\)[/tex], we have:
[tex]\[
9x^2 + 24x + 27
\][/tex]

3. Add the terms from the two distributions together:
- Combine like terms:
- [tex]\(3x^3\)[/tex] (no like term here)
- [tex]\(8x^2 + 9x^2 = 17x^2\)[/tex]
- [tex]\(9x + 24x = 33x\)[/tex]
- [tex]\(27\)[/tex] (no like term here)

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

Therefore, the correct answer is option C: [tex]\(3x^3 + 17x^2 + 33x + 27\)[/tex].

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