Question

Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 3x + 2x2 – 6

Answer 1

To write the polynomial in standard form, rearrange the terms by degree to get 2x^2 + 3x - 6. It is named a second-degree trinomial because the highest degree is 2 and it has three terms.

Step-by-step explanation:

To write the given polynomial 3x + 2x2 – 6 in standard form, we reorder the terms by degree from highest to lowest. So, the standard form is 2x2 + 3x – 6.

Next, we name the polynomial based on its degree and the number of terms. Since the highest power of the variable x is 2, this is a second-degree polynomial. Additionally, there are three terms, so it is called a trinomial. Therefore, the polynomial 2x2 + 3x – 6 is a second-degree trinomial.

Answer 2

So writing a polynomial in standard form is just combining all like terms and then rearranging those terms in descending order of degree. In this case, the term with the highest degree is 2x^2, then 3x, then -6, so our standard form polynomial is
`2x^2+3x-6`

Next, since there are three terms in this polynomial, this would be classified as a trinomial (tri = 3). Now to find the degree of this polynomial, just take the total number of exponents from the highest term, which in this case its 2x^2 with a total of 2. Putting it all together, this polynomial is a 2nd degree trinomial.