# How do you write a polynomial in standard form, then classify it by degree and number of terms  5a+2a^2+a+a^4?

Dec 26, 2017

First, you have to classify the polynomial by its degree. You have to understand the degree of each term of the polynomial.
Let's take your example: $5 a + 2 {a}^{2} + a + {a}^{4}$
The terms here are:
5a, $2 {a}^{2}$, a, and ${a}^{4}$.

The degree of 5a is one. The degree of the term is actually the sum of exponents of the variable.Here, the variable is a, and it is raised to the power of 1.
Thus, the degree of 5a is 1.

Similarly, the degree of $2 {a}^{2}$ is 2; as a(VARIABLE) is raised to the power of 2.

Also, the degree of a is 1, and the degree of ${a}^{4}$ is 4.

Now, if you arrange the term in descending order of their degrees,
you get the standard form of the polynomial.

Thus, here, the standard form of the polynomial is:
${a}^{4} + 2 {a}^{2} + 5 a + a$

And you simplify the polynomial as:
${a}^{4} + 2 {a}^{2} + 6 a$

Of course, there are three terms in this polynomial (${a}^{4} , 2 {a}^{2} , \mathmr{and} 6 a$).

Hope you got it...........
Sorry for the REALLY LOOOOOONG explanation.