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Answer :
Sure! Let's multiply the polynomials step by step.
We have two polynomials: [tex]\( (x + 3) \)[/tex] and [tex]\( (3x^2 + 8x + 9) \)[/tex].
To multiply these, we use the distributive property which involves multiplying each term in the first polynomial by each term in the second polynomial:
1. Multiply [tex]\( x \)[/tex] by each term in the second polynomial:
- [tex]\( x \cdot 3x^2 = 3x^3 \)[/tex]
- [tex]\( x \cdot 8x = 8x^2 \)[/tex]
- [tex]\( x \cdot 9 = 9x \)[/tex]
2. Multiply [tex]\( 3 \)[/tex] by each term in the second polynomial:
- [tex]\( 3 \cdot 3x^2 = 9x^2 \)[/tex]
- [tex]\( 3 \cdot 8x = 24x \)[/tex]
- [tex]\( 3 \cdot 9 = 27 \)[/tex]
Now, let's combine all the terms:
- [tex]\( 3x^3 \)[/tex] (from [tex]\( x \cdot 3x^2 \)[/tex])
- [tex]\( 8x^2 + 9x^2 = 17x^2 \)[/tex] (combine the [tex]\( x^2 \)[/tex] terms)
- [tex]\( 9x + 24x = 33x \)[/tex] (combine the [tex]\( x \)[/tex] terms)
- [tex]\( 27 \)[/tex] (constant term)
So the resulting polynomial is [tex]\( 3x^3 + 17x^2 + 33x + 27 \)[/tex].
The correct answer is C. [tex]\(3x^3 + 17x^2 + 33x + 27\)[/tex].
We have two polynomials: [tex]\( (x + 3) \)[/tex] and [tex]\( (3x^2 + 8x + 9) \)[/tex].
To multiply these, we use the distributive property which involves multiplying each term in the first polynomial by each term in the second polynomial:
1. Multiply [tex]\( x \)[/tex] by each term in the second polynomial:
- [tex]\( x \cdot 3x^2 = 3x^3 \)[/tex]
- [tex]\( x \cdot 8x = 8x^2 \)[/tex]
- [tex]\( x \cdot 9 = 9x \)[/tex]
2. Multiply [tex]\( 3 \)[/tex] by each term in the second polynomial:
- [tex]\( 3 \cdot 3x^2 = 9x^2 \)[/tex]
- [tex]\( 3 \cdot 8x = 24x \)[/tex]
- [tex]\( 3 \cdot 9 = 27 \)[/tex]
Now, let's combine all the terms:
- [tex]\( 3x^3 \)[/tex] (from [tex]\( x \cdot 3x^2 \)[/tex])
- [tex]\( 8x^2 + 9x^2 = 17x^2 \)[/tex] (combine the [tex]\( x^2 \)[/tex] terms)
- [tex]\( 9x + 24x = 33x \)[/tex] (combine the [tex]\( x \)[/tex] terms)
- [tex]\( 27 \)[/tex] (constant term)
So the resulting polynomial is [tex]\( 3x^3 + 17x^2 + 33x + 27 \)[/tex].
The correct answer is C. [tex]\(3x^3 + 17x^2 + 33x + 27\)[/tex].
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