Question

How do we write the polynomial in standard form, then classify it by degree and number of terms \[x + 2{x^2}\]?

Answer 1

Hint: In the given question, we have been given a polynomial which is to be written in its standard form. To do that, we write the terms in order such that the term with the biggest exponent comes first and goes on decreasing. Then we have to write its degree and the number of terms in it.

Complete step by step answer:
To write a polynomial in standard form, we write the terms in order such that the term with the biggest exponent comes first and goes on decreasing.
Hence, \[x + 2{x^2}\] in standard form is
\[2{x^2} + x\]
To classify a polynomial by degree, we look at the highest exponent or degree. Since 2 is the highest exponent, it is quadratic. Here is the first few highest exponent:
1 - linear
2 - quadratic
3 - cubic
4 - quartic
5 - quintic
To classify a polynomial by the number of terms, count how many terms are in the polynomial: In this polynomial, there are two terms. So, this is a binomial.
1 term- monomial
2 terms- binomial
3 terms- trinomial
4+ terms- polynomial

Note:
In the given question, we had to write a polynomial in standard form, then classify it by degree and number of terms. We write in standard form by writing the polynomial in a way that the exponents are in decreasing order. For classifying it by degree and number of terms, we have to remember the names, there is no other way.