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

Standard form
`4x^3-3x+6`

Name the polynomial based on its degree is cubic polynomial

Name the polynomial based on number of terms is trinomial.

Explanation:

Consider the given polynomial
`6-2x^3-3x+6x^3`

We have to write the polynomial in standard form and Then name the polynomial based on its degree and number of terms.

Consider the given polynomial
`6-2x^3-3x+6x^3`

We first simplify the given polynomial by adding like terms,

LIKE TERMS are term having same variable with same power.

Here,
`-2x^3 \ and\ 6x^3` are like terms,

Thus adding both we get,
`4x^3`

Thus, polynomial becomes,
`6+4x^3-3x`

In standard form, terms are arranged in decreasing order of power of variables.

`6+4x^3-3x` can be written as
`4x^3-3x+6`

Thus, the given polynomial has highest power of 3 so its a cubic polynomial on the basis of degree.

and Since, it consist of three terms so it is a trinomial on the basis of number of terms.

Answer 2

6 - 2x^3 - 3x + 6x^3 = 4x^3 - 3x + 6

This is a polynomial of degree 3 with 3 terms