Consider the polynomial 12x Superscript 7minus3x Superscript 6plussix sevenths

Question

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​(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 \( 12x^7 - 3x^6 + \frac{6}{7} \), let's break it down.

Part 1: Degree of the polynomial

The degree of a polynomial is determined by the term with the highest exponent. In this case, the term with the highest exponent is \( 12x^7 \), which has an exponent of 7.

So, the degree of the polynomial is 7.

Part 2: Leading coefficient

The leading coefficient is the coefficient of the term with the highest degree. Here, the leading term is \( 12x^7 \), and the coefficient is 12.

Thus, the leading coefficient is 12.

To summarize:

• (a) The degree of the polynomial is 7.
• (b) The leading coefficient is 12.