Question

question 9 of 20
which of the following expressions are monomials with a degree 2? i) $2x^2 + 2x$, ii) $2x^2$, iii) $x^2$, iv) $2x$
select the correct response:
i, ii, and iii
i and iii
ii and iv
i and ii
none of the above
ii, iii and iv
i and iv
ii and iii

Explanation:

Step1: Recall Monomial and Degree

A monomial is a single term (product of constants and variables), degree is the sum of variable exponents.

• I: \(2x^2 + 2x\)

It has two terms (\(2x^2\) and \(2x\)), so it's a binomial (not a monomial).

• II: \(2x^2\)

Single term, variable exponent \(2\) → monomial, degree \(2\).

• III: \(x^2\)

Single term, variable exponent \(2\) → monomial, degree \(2\).

• IV: \(2x\)

Single term, variable exponent \(1\) → monomial, degree \(1\) (not degree \(2\)).

Step2: Identify Valid Monomials

Only II (\(2x^2\)) and III (\(x^2\)) are monomials with degree \(2\). Wait, wait—wait, the options: let's check again. Wait, the option "II and III"—wait, looking at the options, the last option is "II and III"? Wait, the options given: the last one is "II and III"? Wait, the user's options:

Wait the options are:

• I, II, and III
• I and III
• II and IV
• I and II
• None of the above
• II, III and IV
• I and IV
• II and III

Ah, "II and III" is an option (the last one). So II (\(2x^2\)) is degree 2 monomial, III (\(x^2\)) is degree 2 monomial. I is binomial, IV is degree 1. So II and III are correct.

Answer:

II and III (the last option: II and III)