# How do you write a polynomial in standard form, then classify it by degree and number of terms 2b^2 – 4b^3 + 6?

Apr 10, 2018

Standard Form: $- 4 {b}^{3} + 2 {b}^{2} + 6$
Degree: 3
Num. Terms: 3

#### Explanation:

The standard form of a polynomial is ${C}_{1} {x}^{n} + {C}_{2} {x}^{n - 1} + \ldots + + {C}_{n} x + {C}_{n + 1}$, where each ${C}_{j}$ is a constant. This is not as complicated as it looks. You simply write the polynomial with decreasing terms of your variable, from left to right.

So $2 {b}^{2} - 4 {b}^{3} + 6$ in standard form is $- 4 {b}^{3} + 2 {b}^{2} + 6$. Note that with each term, the degree of $b$ decreases.

The degree of a term is the highest exponent affecting the variable. So $2 {x}^{7}$ has a degree of $7$. Also, $1000 x = 1000 {x}^{1}$ has a degree of $1$. A constant, like $8$, has a degree of $0$.

The degree of a polynomial corresponds to the term in it which has the highest degree. In our case, $- 4 {b}^{3} + 2 {b}^{2} + 6$ has a degree of $3$, because $- 4 {b}^{3}$ has a degree of $3$.

The number of terms in a polynomial is the number of "things" being added together. Here, we have $3$ "things" be added together, with those "things" being $- 4 {b}^{3}$, $2 {b}^{2}$ and $6$.