write the polynomial in standard form then name the polynomial based on its degrees and number of terms
6x^2 + 6x^4 - 2x^2
well, 6-2 = 4, so that leaves 4x^2
then arrange in descending powers of x
6x^2 + 6x^4 - 2x^2 = 6x^4 + 4x^2. So we have a 4th - degree binomial.
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."