Consider the polynomial 6x Superscript 7minus4x Superscript 6plustwo fifths

Question

.
​(a) Give the degree of the polynomial.
​(b) Give the leading coefficient.
Question content area bottom
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 \( 6 \).

---

Summary:

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