Question

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

Answer 1

Standard Form: `-4b^3 + 2b^2 + 6`
Degree: 3
Num. Terms: 3

Explanation:

The standard form of a polynomial is `C_1 x^n + C_2x^(n-1) + ... + + 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 `2b^2 - 4b^3 + 6` in standard form is `-4b^3 + 2b^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 `2x^7` has a degree of `7`. Also, `1000x = 1000x^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, `-4b^3 + 2b^2 + 6` has a degree of `3`, because `-4b^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 `-4b^3`, `2b^2` and `6`.