Deajexidn
Answered

IDNLearn.com: Your trusted source for finding accurate answers. Our experts are available to provide in-depth and trustworthy answers to any questions you may have.

explain why the polynomial 3⁴-8x³+6x²-3x has a degree 3 and not 4​​

Sagot :

Djtwinx017idn

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.

We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for visiting IDNLearn.com. We’re here to provide clear and concise answers, so visit us again soon.