Question

which of the following are terms in this expression? select all that apply.
$n + 3n^3 + k^2 + 5$
options: $k^2$, $3n^3$, $n$, $4$ (with checkmarks on them)

Explanation:

Step1: Recall the definition of a term

A term in an algebraic expression is a single number, variable, or the product of numbers and variables, separated by addition or subtraction signs.

Step2: Analyze each part of the expression \( n + 3n^{3}+k^{2}+5 \)

• For \( n \): It is a single variable, so it is a term.
• For \( 3n^{3} \): It is a product of a number (3) and a variable raised to a power (\( n^{3} \)), so it is a term.
• For \( k^{2} \): It is a single variable raised to a power, so it is a term.
• For the constant term: The constant term in the expression is 5, not 4, so "4" is not a term of the given expression.

Answer:

The correct terms in the expression \( n + 3n^{3}+k^{2}+5 \) are \( k^{2} \), \( 3n^{3} \), \( n \). The term "4" is incorrect as the constant term is 5, not 4. So the correct selected terms should be \( k^{2} \), \( 3n^{3} \), \( n \), and the constant term should be 5 (if an option for 5 was present, but based on the given options with a wrong "4", the right ones among the shown are \( k^{2} \), \( 3n^{3} \), \( n \)).