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lara31 [8.8K]
3 years ago
13

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

Mathematics
1 answer:
Naily [24]3 years ago
5 0

Answer:

The polynomial <u>has a degree of 3</u> because the leading term is -8x³.

Step-by-step explanation:

<h2>Definitions:</h2>
  • A <u>term</u> is the product of a number and one or more variables raised to an exponent.
  • The <u>degree of a term</u> pertains to the exponent of a variable in a term.  
  • The <u>degree of a polynomial</u>  is the highest exponent in a polynomial. Regardless of the value or sign of its coefficient, what matters is the  the <u>exponent</u> of the variable.
  • The term that has the greatest exponent in a polynomial is referred to as the <u>leading term</u>; the coefficient in a leading term is known as the <u>leading coefficient</u>.
<h2>Explanation:</h2>

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 <u>has a degree of 3</u>.

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