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

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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.

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