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Answer :
To multiply the polynomials [tex]\((x + 3)(3x^2 + 8x + 9)\)[/tex], follow these steps:
1. Distribute each term in the first polynomial with each term in the second polynomial:
- Multiply [tex]\(x\)[/tex] by each term in [tex]\(3x^2 + 8x + 9\)[/tex]:
- [tex]\(x \cdot 3x^2 = 3x^3\)[/tex]
- [tex]\(x \cdot 8x = 8x^2\)[/tex]
- [tex]\(x \cdot 9 = 9x\)[/tex]
- Multiply [tex]\(3\)[/tex] by each term in [tex]\(3x^2 + 8x + 9\)[/tex]:
- [tex]\(3 \cdot 3x^2 = 9x^2\)[/tex]
- [tex]\(3 \cdot 8x = 24x\)[/tex]
- [tex]\(3 \cdot 9 = 27\)[/tex]
2. Combine all the results:
[tex]\[
3x^3 + 8x^2 + 9x + 9x^2 + 24x + 27
\][/tex]
3. Combine like terms:
- 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]
4. Write down the simplified polynomial:
[tex]\[
3x^3 + 17x^2 + 33x + 27
\][/tex]
The result is [tex]\(3x^3 + 17x^2 + 33x + 27\)[/tex], which matches option B.
1. Distribute each term in the first polynomial with each term in the second polynomial:
- Multiply [tex]\(x\)[/tex] by each term in [tex]\(3x^2 + 8x + 9\)[/tex]:
- [tex]\(x \cdot 3x^2 = 3x^3\)[/tex]
- [tex]\(x \cdot 8x = 8x^2\)[/tex]
- [tex]\(x \cdot 9 = 9x\)[/tex]
- Multiply [tex]\(3\)[/tex] by each term in [tex]\(3x^2 + 8x + 9\)[/tex]:
- [tex]\(3 \cdot 3x^2 = 9x^2\)[/tex]
- [tex]\(3 \cdot 8x = 24x\)[/tex]
- [tex]\(3 \cdot 9 = 27\)[/tex]
2. Combine all the results:
[tex]\[
3x^3 + 8x^2 + 9x + 9x^2 + 24x + 27
\][/tex]
3. Combine like terms:
- 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]
4. Write down the simplified polynomial:
[tex]\[
3x^3 + 17x^2 + 33x + 27
\][/tex]
The result is [tex]\(3x^3 + 17x^2 + 33x + 27\)[/tex], which matches option B.
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