High School

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Combine the like terms in the polynomials below:

[tex]\left(4+2x^3\right)+\left(5x^3+2\right)[/tex]

A. [tex]-7x^3 + 6[/tex]
B. [tex]7x^3 + 6[/tex]
C. [tex]7x^3 - 6[/tex]
D. None

Answer :

To combine the like terms in the polynomials [tex]\((4 + 2x^3) + (5x^3 + 2)\)[/tex], follow these steps:

1. Identify the like terms:
- The constant terms are [tex]\(4\)[/tex] and [tex]\(2\)[/tex].
- The [tex]\(x^3\)[/tex] terms are [tex]\(2x^3\)[/tex] and [tex]\(5x^3\)[/tex].

2. Combine the constant terms:
- Add [tex]\(4\)[/tex] and [tex]\(2\)[/tex] together:
[tex]\[
4 + 2 = 6
\][/tex]

3. Combine the [tex]\(x^3\)[/tex] terms:
- Add the coefficients of the [tex]\(x^3\)[/tex] terms:
[tex]\[
2x^3 + 5x^3 = 7x^3
\][/tex]

4. Write the combined polynomial:
- The simplified expression, after combining all the like terms, is:
[tex]\[
7x^3 + 6
\][/tex]

So, the correct choice from the given options is [tex]\(7x^3 + 6\)[/tex].

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