College

Choose the correct simplification of [tex]\left(4x^3 - 3x - 7\right) + \left(3x^3 + 5x + 3\right)[/tex].

A. [tex]7x^3 - 2x - 4[/tex]
B. [tex]x^3 - 8x - 10[/tex]
C. [tex]7x^3 + 2x - 4[/tex]
D. [tex]x^3 + 8x + 10[/tex]

Answer :

To simplify
[tex]$$\left(4x^3 - 3x - 7\right) + \left(3x^3 + 5x + 3\right),$$[/tex]
follow these steps:

1. Combine the cubic terms ([tex]$x^3$[/tex]):

The cubic term in the first polynomial is [tex]$4x^3$[/tex] and in the second is [tex]$3x^3$[/tex]. Adding these gives:
[tex]$$4x^3 + 3x^3 = 7x^3.$$[/tex]

2. Combine the linear terms ([tex]$x$[/tex]):

The linear term in the first polynomial is [tex]$-3x$[/tex] and in the second is [tex]$5x$[/tex]. Adding these gives:
[tex]$$-3x + 5x = 2x.$$[/tex]

3. Combine the constant terms:

The constant in the first polynomial is [tex]$-7$[/tex] and in the second is [tex]$3$[/tex]. Adding these gives:
[tex]$$-7 + 3 = -4.$$[/tex]

4. Write the final simplified polynomial:

Putting it all together, we obtain:
[tex]$$7x^3 + 2x - 4.$$[/tex]

Thus, the correct simplification is
[tex]$$\boxed{7x^3 + 2x - 4}.$$[/tex]