well, 6-2 = 4, so that leaves 4x^2
then arrange in descending powers of x
6x^2 + 6x^4 - 2x^2
then arrange in descending powers of x
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."