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What is [tex]\left(3x^4 + 2 - 2x^3\right) + \left(4x^3 + 4x^4\right)[/tex]?

A. [tex]7x^4 + 7x^3 + 2[/tex]

B. [tex]7x^7 + 2x + 2[/tex]

C. [tex]7x^4 + 2x^3 + 2[/tex]

D. [tex]7x^7 + x^6 + 2[/tex]

Answer :

We start with the expression

[tex]$$
(3x^4 + 2 - 2x^3) + (4x^3 + 4x^4).
$$[/tex]

Step 1: Rearrange the terms to group like terms together. Write the [tex]$x^4$[/tex] terms, the [tex]$x^3$[/tex] terms, and the constant separately:

[tex]$$
3x^4 + 4x^4 - 2x^3 + 4x^3 + 2.
$$[/tex]

Step 2: Combine the [tex]$x^4$[/tex] terms:

[tex]$$
3x^4 + 4x^4 = 7x^4.
$$[/tex]

Step 3: Combine the [tex]$x^3$[/tex] terms:

[tex]$$
-2x^3 + 4x^3 = 2x^3.
$$[/tex]

Step 4: The constant term remains as is:

[tex]$$
2.
$$[/tex]

Step 5: Write the resulting expression by putting all the combined terms together:

[tex]$$
7x^4 + 2x^3 + 2.
$$[/tex]

Thus, the simplified polynomial is

[tex]$$
7x^4 + 2x^3 + 2.
$$[/tex]

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