Question

Which description is correct for the polynomial −5x2−3x+3 ?

1)quartic binomial

2)cubic binomial

3)quadratic binomial

4)quadratic trinomial

Which description is correct for the polynomial −5x3−4x+1 ?



1)cubic monomial

2)cubic binomial

3)cubic trinomial

4)quadratic trinomial

What is the degree of the polynomial 3xy^2z−2z^5+2/3y^2z^4 ?



1)2

2)4

3)5

4)6

Answer 1

The degree of a polynomial is the highest power of its terms. In the polynomial $-5x^2 - 3x + 3$, the degree of the polynomial is 2.

There is also a name to each degree of a polynomial:
Degree 0 – constant
Degree 1 – linear
Degree 2 – quadratic
Degree 3 – cubic
Degree 4 – quartic
Degree 5 – quintic
You will probably not deal with polynomials after a degree of 5, but they will usually be called an nth-degree polynomial (e.g., 10th degree polynomial).

You can further classify polynomials according to the number of terms.
1 term: monomial (techinically not a polynomial as a polynomial consists of 2 or more monomials)
2 terms: binomial
3 terms: trinomial
After 3 terms, the polynomial is called a polynomial of n terms (e.g., polynomial of 4 terms).

So for the polynomial $-5x^3 - 4x + 1$, its highest power is 3, so its degree is 3. It also has 3 terms, making it a cubic trinomial.

Answer 2

Answer:

   

Step-by-step explanation:

A. The given polynomial is:

$-5x^2-3x+3$

Since, degree is the highest power of the polynomial, thus the degree of the given polynomial is 2, since 2 is the highest power.

Also, the given polynomial consists of three terms, thus it is a trinomial.

Hence, the given polynomial is Quadratic trinomial.

Option(4) is correct.

B. The given polynomial is:

$-5x^3-4x+1$

The degree of the given polynomial is 3 since 3 is the highest power of the polynomial, also the polynomial consists of three terms.

Thus, the given polynomial is Cubic trinomial.

Option (3) is correct.

C. The given polynomial is:

$3xy^2z-2z^5+\frac{2}{3}y^2z^4$

The highest power of the given polynomial is 6, thus the degree of the given polynomial will be 6.