list the terms, coeffcients, and degree of the following polynomial:x^4+6x^3-x+3/4
To identify the terms, coefficients, and degree of the polynomial x^4 + 6x^3 - x + 3/4, we need to understand each of these concepts:
1. Terms: In a polynomial, a term is a part that consists of a variable raised to a power, multiplied by a coefficient. Terms are usually separated by a plus (+) or minus (-) sign.
2. Coefficients: The coefficient is the numerical value that multiplies the variable in each term. It indicates the magnitude or scale of each term.
3. Degree: The degree of a polynomial is the highest exponent/power of the variable in any term within the polynomial.
Now, let's break down the given polynomial step by step:
x^4 + 6x^3 - x + 3/4
Terms:
The terms in this polynomial are: x^4, 6x^3, -x, and 3/4.
Coefficients:
The coefficients in this polynomial are: 1, 6, -1, and 3/4.
Degree:
To determine the degree, we simply look for the term with the highest exponent on the variable. In this case, the term with the highest exponent is x^4. Hence, the degree of the polynomial is 4.
So, the terms, coefficients, and degree of the polynomial x^4 + 6x^3 - x + 3/4 are as follows:
- Terms: x^4, 6x^3, -x, 3/4
- Coefficients: 1, 6, -1, 3/4
- Degree: 4