High School

Two polynomials are shown:

A: [tex]3x^3 + 7[/tex]
B: [tex]7x + 3[/tex]

What is the resulting polynomial of [tex]A \times B[/tex]?

A. [tex]21x^4 + 49x[/tex]
B. [tex]3x^3 + 7x + 10[/tex]
C. [tex]21x^4 + 9x^3 + 49x + 21[/tex]
D. [tex]21x^4 + 21x^3 + 21x + 21[/tex]

Answer :

To find the resulting polynomial when multiplying polynomials [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we follow these steps:

1. Identify the polynomials:
- Polynomial [tex]\(A\)[/tex] is [tex]\(3x^3 + 7\)[/tex].
- Polynomial [tex]\(B\)[/tex] is [tex]\(7x + 3\)[/tex].

2. Multiply each term in Polynomial [tex]\(A\)[/tex] by each term in Polynomial [tex]\(B\)[/tex]:

[tex]\[
(3x^3 + 7) \times (7x + 3)
\][/tex]

3. Distribute the terms from Polynomial [tex]\(A\)[/tex] with Polynomial [tex]\(B\)[/tex]:

- Multiply [tex]\(3x^3\)[/tex] by [tex]\(7x\)[/tex] to get [tex]\(21x^4\)[/tex].
- Multiply [tex]\(3x^3\)[/tex] by [tex]\(3\)[/tex] to get [tex]\(9x^3\)[/tex].
- Multiply [tex]\(7\)[/tex] by [tex]\(7x\)[/tex] to get [tex]\(49x\)[/tex].
- Multiply [tex]\(7\)[/tex] by [tex]\(3\)[/tex] to get [tex]\(21\)[/tex].

4. Combine all the terms:

The resulting polynomial from the multiplication and combining the above terms is:

[tex]\[
21x^4 + 9x^3 + 49x + 21
\][/tex]

This is the polynomial representation of the product of [tex]\(A\)[/tex] and [tex]\(B\)[/tex]. Therefore, the correct choice is:

[tex]\[
21x^4 + 9x^3 + 49x + 21
\][/tex]

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