High School

What is the simplest form of [tex]\left(4x^3 + 6x - 7\right) + \left(3x^3 - 5x^2 - 5x\right)[/tex]?

A. [tex]7x^3 - 5x^2 + x - 7[/tex]
B. [tex]7x^6 - 4x^2 - 7[/tex]
C. [tex]7x^3 + x^2 - 5x - 7[/tex]
D. [tex]7x^3 - 5x^2 - x - 7[/tex]

Answer :

We begin by writing the sum of the two polynomials:

[tex]$$
(4x^3 + 6x - 7) + (3x^3 - 5x^2 - 5x)
$$[/tex]

Next, we group and combine like terms.

1. The cubic terms:
[tex]$$
4x^3 + 3x^3 = 7x^3
$$[/tex]

2. The quadratic term:
[tex]$$
-5x^2 \quad \text{(there is no other quadratic term)}
$$[/tex]

3. The linear terms:
[tex]$$
6x - 5x = x
$$[/tex]

4. The constant term:
[tex]$$
-7 \quad \text{(there is no other constant term)}
$$[/tex]

Putting it all together, the simplified form of the expression is:

[tex]$$
7x^3 - 5x^2 + x - 7
$$[/tex]

Thus, the simplest form of the given expression is:

[tex]$$
\boxed{7x^3 - 5x^2 + x - 7}
$$[/tex]