Answer:
The polynomial has a degree of 3 because the leading term is -8x³.
Step-by-step explanation:
Definitions:
- A term is the product of a number and one or more variables raised to an exponent.
- The degree of a term pertains to the exponent of a variable in a term.
- The degree of a polynomial is the highest exponent in a polynomial. Regardless of the value or sign of its coefficient, what matters is the the exponent of the variable.
- The term that has the greatest exponent in a polynomial is referred to as the leading term; the coefficient in a leading term is known as the leading coefficient.
Explanation:
Given the following polynomial: 3⁴- 8x³+ 6x²- 3x:
If we rearrange this in descending degree, it will be easier to understand why the given polynomial has a degree of 3:
3⁴- 8x³+ 6x²- 3x ⇒ - 8x³+ 6x²- 3x + 3⁴
"3⁴" is not a term. It is referred to as a constant. 3⁴ = 3 × 3 × 3 × 3 = 81.
We can substute 3⁴ = 81 into the polynomial:
- 8x³+ 6x²- 3x + 81
As we can see, the term with the highest degree is -8x³. Therefore, the polynomial has a degree of 3.
