Question

polynomial terms and standard form
score 0/10 penalty: 1 off
question
determine if the expression (-x^{4}y^{2}sqrt{2}) is a polynomial or not. if it is a polynomial, state the type and degree of the polynomial.
answer attempt 1 out of 2
the given expression dropdown a polynomial.
dropdown options: represents, does not represent

Explanation:

Step1: Recall the definition of a polynomial

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables. In the expression \(-x^{4}y^{2}\sqrt{2}\), we have variables \(x\) and \(y\) with exponents \(4\) and \(2\) respectively (which are non - negative integers), and the coefficient \(-\sqrt{2}\). The operations involved are multiplication (of the coefficient with the variables and between the variables). So this expression satisfies the definition of a polynomial.

Step2: Determine the type of polynomial

A polynomial with only one term is called a monomial. Since the expression \(-x^{4}y^{2}\sqrt{2}\) has only one term, it is a monomial.

Step3: Calculate the degree of the polynomial

The degree of a term in a polynomial with multiple variables is the sum of the exponents of the variables in that term. For the term \(-x^{4}y^{2}\sqrt{2}\), the exponent of \(x\) is \(4\) and the exponent of \(y\) is \(2\). So the degree of the term is \(4 + 2=6\). Since this is a monomial (a polynomial with one term), the degree of the polynomial is equal to the degree of its single term, which is \(6\).

Answer:

The given expression \(\boldsymbol{\text{represents}}\) a polynomial. It is a monomial with degree \(6\).