Question

question 2
which description is correct for the polynomial?
$3x^3 + 4x^2 - 7$
○ quadratic trinomial
○ quartic trinomial
○ cubic binomial
○ cubic trinomial

Explanation:

Step1: Determine the degree of the polynomial

The degree of a polynomial is the highest power of the variable. In the polynomial \(3x^{3}+4x^{2}-7\), the highest power of \(x\) is \(3\) (from the term \(3x^{3}\)). So the degree is \(3\), which means it is a cubic polynomial.

Step2: Determine the number of terms

A term is a single number or a product of a number and variables. The polynomial \(3x^{3}+4x^{2}-7\) has three terms: \(3x^{3}\), \(4x^{2}\), and \(-7\). A polynomial with three terms is called a trinomial.

Step3: Match the type

Combining the degree (cubic) and the number of terms (trinomial), the polynomial \(3x^{3}+4x^{2}-7\) is a cubic trinomial.

Answer:

cubic trinomial (assuming the last option is "cubic trinomial" as per the partial text in the image)