First, let's start by writing the given polynomial in its standard form:
5x^2 - 4 + 6x
The standard form of a polynomial arranges the terms by degree in descending order. So here, the standard form will be:
5x^2 + 6x - 4
The degree of a polynomial is determined by the highest power of the variable within the polynomial. In this case, the variable 'x' has the highest power of 2 (from 5x^2), which makes the degree of this polynomial 2.
The number of terms in a polynomial is just how many expressions are being added, subtracted, or are standing alone. Here, we're dealing with three expressions - 5x^2, 6x, and -4. So the number of terms is 3.
Lastly, we use the number of terms to classify the type of polynomial:
- If there is 1 term, it's a monomial.
- If there are 2 terms, it's a binomial.
- If there are 3 terms, it's a trinomial.
- If there are 4 or more terms, it's just generally referred to as a polynomial.
So for our given equation, since there are 3 terms, it would be classified as a trinomial.
So to sum it all up:
- The standard form of the given polynomial is 5x^2 + 6x - 4.
- The degree of the polynomial is 2.
- The number of terms in the polynomial is 3.
- The polynomial would be classified as a trinomial.