Question

find the number of terms and the degree of this polynomial.\\(-4t^3 + 10t^4 + 5t^2\\)\
number of terms: \\(\square\\)\
degree: \\(\square\\)

Explanation:

Step1: Count the number of terms

A term in a polynomial is a single number, variable, or the product of numbers and variables separated by addition or subtraction. In the polynomial \(-4t^3 + 10t^4 + 5t^2\), the terms are \(-4t^3\), \(10t^4\), and \(5t^2\). So we count them: 1. \(-4t^3\), 2. \(10t^4\), 3. \(5t^2\). So the number of terms is 3.

Step2: Determine the degree of the polynomial

The degree of a polynomial is the highest power (exponent) of the variable in the polynomial. For each term:

• The term \(-4t^3\) has a degree of 3 (the exponent of \(t\) is 3).
• The term \(10t^4\) has a degree of 4 (the exponent of \(t\) is 4).
• The term \(5t^2\) has a degree of 2 (the exponent of \(t\) is 2).

We compare these degrees: 3, 4, and 2. The highest among them is 4. So the degree of the polynomial is 4.

Answer:

Number of terms: 3
Degree: 4