High School

Resuelve la resta [tex]\left(x^3+2x^2+10\right)-\left(-6x^3-7x^2-5\right)[/tex].

Escoge una respuesta:

A. [tex]-5x^3+2x^2+10[/tex]

B. [tex]7x^3+9x^2+15[/tex]

C. [tex]7x^3+2x^2+10[/tex]

D. [tex]5x^3-2x^2-5[/tex]

Answer :

We start with the expression

[tex]$$
\left(x^3 + 2x^2 + 10\right) - \left(-6x^3 - 7x^2 - 5\right).
$$[/tex]

The first step is to distribute the minus sign to the second polynomial:

[tex]$$
(x^3 + 2x^2 + 10) + (6x^3 + 7x^2 + 5).
$$[/tex]

Next, we combine like terms. For the [tex]$x^3$[/tex] terms, we have:

[tex]$$
x^3 + 6x^3 = 7x^3.
$$[/tex]

For the [tex]$x^2$[/tex] terms:

[tex]$$
2x^2 + 7x^2 = 9x^2.
$$[/tex]

Finally, for the constant terms:

[tex]$$
10 + 5 = 15.
$$[/tex]

Thus, the expression simplifies to:

[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]

So, the correct answer is

[tex]$$
7x^3 + 9x^2 + 15.
$$[/tex]