Question

write the polynomial in standard form then name the polynomial based on its degrees and number of terms

6x^2 + 6x^4 - 2x^2

Answer 1

well, 6-2 = 4, so that leaves 4x^2

then arrange in descending powers of x

Answer 2

6x^2 + 6x^4 - 2x^2 = 6x^4 + 4x^2. So we have a 4th - degree binomial.

Answer 3

[AI-generated answer — Explain Bot]

To write the polynomial in standard form, we need to combine like terms and arrange the terms in decreasing order of their exponents.

First, let's combine the like terms:

6x^2 + 6x^4 - 2x^2

Combining the like terms (6x^2 and -2x^2), we get:

(6x^4 + 6x^2) - 2x^2

Simplifying further, we have:

(6x^4 + 6x^2 - 2x^2)

Now, let's arrange the terms in decreasing order of their exponents:

6x^4 + 6x^2 - 2x^2

This polynomial is already in standard form.

Now let's name the polynomial based on its degrees and number of terms:

The degree of a polynomial is determined by the highest exponent on x. In this case, the highest exponent is 4, so the degree of the polynomial is 4.

The number of terms in a polynomial is determined by counting the individual terms. In this case, we have three terms: 6x^4, 6x^2, and -2x^2. Therefore, the polynomial has 3 terms.

Based on its degree and the number of terms, we can name the polynomial as a "quartic trinomial."