Question

1. which of the following polynomials has three terms?

a. $3x^4 - 5x^2 + x + 8$
b. $4x^3 + 2x$
c. $6x^2 - 2$
d. $x^2 + 5x + 7$

Explanation:

Step1: Recall the definition of a term in a polynomial

A term in a polynomial is a single number, variable, or the product of a number and one or more variables. We need to count the number of terms in each given polynomial.

Step2: Analyze option a

The polynomial \(3x^{4}-5x^{2}+x + 8\) has four terms: \(3x^{4}\), \(-5x^{2}\), \(x\), and \(8\).

Step3: Analyze option b

The polynomial \(4x^{3}+2x\) has two terms: \(4x^{3}\) and \(2x\).

Step4: Analyze option c

The polynomial \(6x^{2}-2\) has two terms: \(6x^{2}\) and \(-2\).

Step5: Analyze option d

The polynomial \(x^{2}+5x + 7\) has three terms: \(x^{2}\), \(5x\), and \(7\).

Answer:

d. \(x^{2}+5x + 7\)