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Answer :
Answer:
B
Step-by-step explanation:
given
([tex]x^{4}[/tex] + 1 )(3x² + 9x + 2 )
Each term in the second factor is multiplied by each term in the first factor, that is
[tex]x^{4}[/tex] (3x² + 9x + 2 ) + 1(3x² + 9x + 2 ) ← distribute parenthesis
= 3[tex]x^{6}[/tex] + 9[tex]x^{5}[/tex] + 2[tex]x^{4}[/tex] + 3x² + 9x + 2
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Rewritten by : Barada
Let's solve the multiplication problem step-by-step:
We need to multiply the polynomials [tex]\((x^4 + 1)\)[/tex] and [tex]\((3x^2 + 9x + 2)\)[/tex].
### Step 1: Distribute each term in [tex]\((x^4 + 1)\)[/tex] with every term in [tex]\((3x^2 + 9x + 2)\)[/tex].
1. Multiply [tex]\(x^4\)[/tex] with each term in the second polynomial:
- [tex]\(x^4 \cdot 3x^2 = 3x^{6}\)[/tex]
- [tex]\(x^4 \cdot 9x = 9x^{5}\)[/tex]
- [tex]\(x^4 \cdot 2 = 2x^{4}\)[/tex]
2. Multiply [tex]\(1\)[/tex] with each term in the second polynomial:
- [tex]\(1 \cdot 3x^2 = 3x^{2}\)[/tex]
- [tex]\(1 \cdot 9x = 9x\)[/tex]
- [tex]\(1 \cdot 2 = 2\)[/tex]
### Step 2: Combine all these products.
The result is formed by adding all these products together:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
So, the expression [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex] simplifies to:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
And that's the final result of multiplying the given polynomials.
We need to multiply the polynomials [tex]\((x^4 + 1)\)[/tex] and [tex]\((3x^2 + 9x + 2)\)[/tex].
### Step 1: Distribute each term in [tex]\((x^4 + 1)\)[/tex] with every term in [tex]\((3x^2 + 9x + 2)\)[/tex].
1. Multiply [tex]\(x^4\)[/tex] with each term in the second polynomial:
- [tex]\(x^4 \cdot 3x^2 = 3x^{6}\)[/tex]
- [tex]\(x^4 \cdot 9x = 9x^{5}\)[/tex]
- [tex]\(x^4 \cdot 2 = 2x^{4}\)[/tex]
2. Multiply [tex]\(1\)[/tex] with each term in the second polynomial:
- [tex]\(1 \cdot 3x^2 = 3x^{2}\)[/tex]
- [tex]\(1 \cdot 9x = 9x\)[/tex]
- [tex]\(1 \cdot 2 = 2\)[/tex]
### Step 2: Combine all these products.
The result is formed by adding all these products together:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
So, the expression [tex]\((x^4 + 1)(3x^2 + 9x + 2)\)[/tex] simplifies to:
[tex]\[ 3x^6 + 9x^5 + 2x^4 + 3x^2 + 9x + 2 \][/tex]
And that's the final result of multiplying the given polynomials.
