Question

Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.
6 – 2x3 – 3x + 6x3

Answer 1

First gather up the like terms and simplify.
Then rearrange the order of the terms from the highest degree to the lowest and finally the constant. This will put the polynomial in standard form.
The degree of a polynomial is the highest degree. If the highest degree is 2 it is called a quadratic, if it is 3 it is cubic, 4 is quartic. Pick the correct name from the list.

Answer 2

I have never learned this so I am really confused

Answer 3

\[6 - 2x ^{3} - 3x + 6x ^{3}\]Collect the like terms. -2x^3 and +6x^3 are like terms and they add up to 4x^3
\[6 + 4x ^{3} - 3x\]Put them from the highest degree to the lowest degree. The exponent tells you the degree.
x^3 is degree 3. x^2 is degree 2. x is degree 1. constant is zero degree. So if I rearrange the polynomial from the highest to the lowest degree I get:
\[4x ^{3} - 3x + 6\]This is the polynomial in standard form.

The highest degree is 3 and so it is a cubic.

There are three terms and so it is a trinomial.

PS:
If there is just one term it is called a monomial. 2 terms is binomial. 3 terms is trinomial. 4 or more terms is just a polynomial of however many terms.

Answer 4

thank you I believe I got it.