4y^2+5 what is the degree for each term? What is the degree for the polynomial? Name the polynomial using both the number of terms and degree. Is the polynomial in standard form?

Question

This is my first time working with polynomials so I don’t know what to do.

Answer 1

So there are two terms here. Terms are the parts of the polynomial that are being added or subtracted. In this case the terms are 4y² and 5. The degree of a polynomial is the highest exponent in the polynomial, so in the polynomial 2x⁴ + 4x³ + 2, the degree would be 4. The degrees of each term is just the exponent on the variable of each term, so in this example, the degree of the first term, 2x⁴ , is 4, the degree of the second term, 4x³, is 3 and the degree of the last term, 2, is 0.

Next, polynomials are named by the number of terms they have and by their degree.

monomial - polynomial with one term

binomial - polynomial with two terms

trinomial - polynomial with three terms

Anything higher with n terms is called an n-term polynomial

linear - polynomial with degree of 1

quadratic - degree of 2

cubic - degree of 3

quartic - degree of 4

For the example 2x⁴ + 4x³ + 2, we have a quartic trinomial.

Lastly, a polynomial is in standard form if the exponents are in descending order from left to right. In the example, the exponents are in descending order (4, 3, 0). So it's in standard form