Question

How do you find the degree and leading coefficient of the polynomial \[14b - 25{b^6}\]?

Answer 1

Hint: Here in this question, we have to find the degree and leading coefficient of a given polynomial. We consider the degree as the highest power of the variable. The leading coefficient is the coefficient of the highest degree. Hence, we obtain the required solution for the given question.

Complete step by step solution:
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables. The degree of a polynomial is identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the leading term and it is usually written first. The coefficient of the leading term is called the leading coefficient.
Now consider the given polynomial \[14b - 25{b^6}\], the highest degree of the given polynomial is 6. The given equation is written in the general form as \[ - 25{b^6} + 14b\]. The coefficient of the highest degree is -25. Therefore the leading coefficient is -25. The coefficients of the polynomial can be either positive or negative.
Therefore the degree and the leading coefficient of the polynomial \[14b - 25{b^6}\] is 6 and -25.
Hence we have obtained the solution.
So, the correct answer is “6 and -25.”.

Note: A polynomial is an algebraic expression where it contains both variables and constants. The degree of the polynomial is identified or determined, when the polynomial has the highest power which is raised to the variable. We must know how to write the polynomial in its general form.