Question

m up: intro to polynomials

1. rewrite the polynomial below in standard form,

then classify it based on its degree and number of terms.
$x^{2}-xy+x+y^{2}$
standard form: ____________
degree: ____________
number of terms: ____________

Explanation:

Step1: Arrange by descending degree

Standard form for multivariable polynomials orders terms by descending sum of variable exponents. The terms $x^2$, $y^2$, $-xy$ all have degree 2, followed by $x$ (degree 1). A valid standard form is:
$x^2 + y^2 - xy + x$

Step2: Find highest term degree

Calculate degree of each term:

• $\deg(x^2)=2$, $\deg(y^2)=2$, $\deg(-xy)=1+1=2$, $\deg(x)=1$

Highest degree is 2.

Step3: Count total distinct terms

Identify each separate term: $x^2$, $-xy$, $x$, $y^2$. Total terms = 4.

Answer:

Standard Form: $x^2 + y^2 - xy + x$
Degree: $2$
Number of Terms: $4$