Question

Find the given sum.

$\left(x^3+2\right)+\left(-3x^3-5\right)$

Short answer

The final answer is $-2x^3-3$.

Step-by-step solution

Step 1. Define standard form of a polynomial.

The standard form of a polynomial means, writing the polynomial in descending powers of the variable.

Step 2. Define like and unlike terms.

In algebra, like terms are the terms that have the same variables and powers.

The unlike terms are two or more terms that are not like terms.

Step 3. Find the sum, x3+2+−3x3−5.

Simplify the given sum by combining the like terms.

$$\begin{gathered} \left(x^3+2\right)+\left(-3x^3-5\right)=x^3+2-3x^3-5 \\ =x^3-3x^3-5+2 \\ =-2x^{}-3 \end{gathered}$$

Therefore the final answer is $-2x^3-3$.