Question

find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these.
$x^{2}y - 2xy^{2}+5x + y^{7}$
the degree of the polynomial is 7.
is $x^{2}y - 2xy^{2}+5x + y^{7}$ a monomial, binomial, trinomial, or none of these?
a. monomial
b. binomial
c. trinomial
d. none of these

Explanation:

Step1: Calculate degree of each term

• Degree of $x^2y$: $2+1=3$
• Degree of $-2xy^2$: $1+2=3$
• Degree of $5x$: $1$
• Degree of $y^7$: $7$

Step2: Identify highest degree

The maximum value from the degrees is $7$.

Step3: Count number of terms

The polynomial $x^2y - 2xy^2 + 5x + y^7$ has 4 distinct terms.

Step4: Classify the polynomial

Monomial (1 term), binomial (2 terms), trinomial (3 terms) do not apply, so it is none of these.

Answer:

The degree of the polynomial is 7.
D. None of these