Question

Consider the polynomial 6x Superscript 7minus4x Superscript 6plustwo fifths
.
​(a) Give the degree of the polynomial.
​(b) Give the leading coefficient.
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Part 1
​(a) The degree of the polynomial is
  
enter your response here. ​(Type a whole​ number.)
Part 2
​(b) The leading coefficient is
  
enter your response here. ​(Type an integer or a​ fraction.)

Answer 1

To analyze the polynomial \( 6x^7 - 4x^6 + \frac{2}{5} \):

### Part 1:
**(a)** The degree of a polynomial is the highest power of the variable \( x \) in the polynomial.

In the polynomial \( 6x^7 - 4x^6 + \frac{2}{5} \), the highest power of \( x \) is \( 7 \).

**Thus, the degree of the polynomial is** \( 7 \).

### Part 2:
**(b)** The leading coefficient is the coefficient of the term with the highest power of \( x \).

In the term \( 6x^7 \), the coefficient of \( x^7 \) is \( 6 \).

**Thus, the leading coefficient is** \( 6 \).

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### Summary:
- Part 1: The degree of the polynomial is \( 7 \).
- Part 2: The leading coefficient is \( 6 \).