Question

introduction to polynomials
which expression is a trinomial of degree 1?
$xy^2$
$x^3 + x^2 - x$
$3x - y$
$6 + x - y$

Explanation:

Step1: Define trinomial & degree

A trinomial has 3 terms; degree is the highest sum of exponents of variables in any term.

Step2: Analyze first option

$xy^2$: 1 term (monomial), degree $1+2=3$. Reject.

Step3: Analyze second option

$x^3+x^2-x$: 3 terms (trinomial), degree 3. Reject.

Step4: Analyze third option

$3x-y$: 2 terms (binomial), degree 1. Reject.

Step5: Analyze fourth option

$6+x-y$: 3 terms (trinomial), highest degree of terms is 1 (for $x$ and $-y$; constant term has degree 0). Accept.

Answer:

$6+x-y$