# How do you write a polynomial in standard form, then classify it by degree and number of terms 8x^2+9+5x^3?

Jul 4, 2017

See below.

#### Explanation:

I am glad you asked this question, it is a very important math concept.

Okay, so whenever you are asked to find the "number of terms," just count the number of terms given (after of course, combining all like terms). For example, let's say you were given ${x}^{2} + 3 + 4$, you would not say that the number of terms is $3$, you would say it is $2$, since you want to add the $3$ and $4$ first. In this particular problem, we have:

$\text{Number of terms} = 3$

Now, we will move on to standard form. Whenever you are asked to write a polynomial in standard form, arrange it in order of decreasing power. In other words, ${x}^{n} > {x}^{n - 1} , \text{... } {x}^{4} > {x}^{3} > {x}^{2} > x > {x}^{0} ,$, so ${x}^{4}$ goes first and ${x}^{0}$ goes last. In this particular problem, $9$ is the ${x}^{0}$ term (so you don't get confused).

If we arrange it according to the definition I gave you, you get:

$5 {x}^{3} + 8 {x}^{2} + 9$

This is the polynomial in standard form.

Lastly, we need to find degree. This is the easiest, as we just have to look at the polynomial in standard form. The first term of the polynomial in standard form will contain ${x}^{n}$, where $n$ is some unknown number. In other words, whatever power $x$ is raised to in standard form will be the degree of the polynomial.

For this particular problem, the $\text{Degree } = 3$, since $x$ is raised to the $3 \text{rd}$ power for the first term of the polynomial in standard form.

That is it, I hope that helps!