Question

combine like terms. write the answer in correct standard form. then list the degree and circle m for monomial, b for binomial, t for trinomial or p if there are more than three terms.

1. ( 3xy^{2}+8xy^{4}+5xy - 2y^{3} )

( 8xy^{4}+1xy^{2}+5xy )
degree =

1. ( 8x^{2}-15x - 21+16x^{2}-4x^{2}y )

( -4x^{2}y + 24x^{2}-15x - 21 )
degree =

1. ( 10x^{2}y+3xy - 4xy^{2}-5xy )

degree =

Explanation:

Step1: Combine like terms

$$\begin{align*} 10x^{2}y+3xy - 4xy^{2}-5xy&=10x^{2}y+(3xy - 5xy)-4xy^{2}\\ &=10x^{2}y-2xy - 4xy^{2} \end{align*}$$

Step2: Find the degree of each term

• For the term \(10x^{2}y\), the degree is \(2 + 1=3\)
• For the term \(-2xy\), the degree is \(1+1 = 2\)
• For the term \(-4xy^{2}\), the degree is \(1+2=3\)

Step3: Determine the degree of the polynomial

The degree of a polynomial is the highest degree of its terms. Here, the highest degree is \(3\)

Step4: Count the number of terms

The polynomial \(10x^{2}y-2xy - 4xy^{2}\) has \(3\) terms, so it is a trinomial

Answer:

degree = \(3\), circle \(T\)