Question

What are the rules for adding,Subtracting, and multiplying polunamjals?

Answer 1

The rules for adding and subtracting polynomials are the same for both operations, you can add or subtract like terms.

Recall that two terms are called like terms if they have the same variables with the same exponents.

For example:

`\begin{gathered} P(x)=x^3+2x^2+x, \\ G(x)=x^2+3. \end{gathered}`

To identify the like terms, we have to observe the variable, which in this case is x, those terms that have the same exponents are like terms.

The like terms are:

`x^2,2x^2\text{.}`

Therefore:

`P(x)+G(x)=x^3+(2x^2+x^2)+x+3=x^3+3x^2+x+3.`
`\begin{gathered} P(x)-G(x)=x^3+2x^2+x-(x^2+3)=x^3+2x^2+x-x^2-3 \\ =x^3+(2x^2-x^2)+x-3=x^3+x^2+x-3. \end{gathered}`