Question

Simplify the expression. What classification describes the resulting polynomial?

(x2 + 7x) + (2x2 − 7x)

A.
linear monomial
B.
linear binomial
C.
quadratic binomial
D.
quadratic monomial

Answer 1

The simplified expression (x^2 + 7x) + (2x^2 − 7x) is 3x^2, which is a quadratic monomial because it contains only one term and the highest power of x is 2.

Step-by-step explanation:

To simplify the expression and classify the resulting polynomial, we need to combine like terms. We have (x2 + 7x) + (2x2 − 7x). Combining like terms, we add the coefficients of x2 terms and x terms separately. The x2 terms (1x2 and 2x2) add up to 3x2, and the x terms (7x and -7x) cancel each other out. Therefore, the simplified expression is 3x2.

Since the resulting expression contains only one term, it is called a monomial, and because the highest power of the variable x is 2, it is also known as a quadratic monomial. Therefore, the correct classification for this polynomial is quadratic monomial (Option D).