Question

What is the leading term, leading coefficient, and degree of this polynomial \[f(x) = 3{x^5} + 6{x^4} - x - 3\] ?

Answer 1

Hint: Here in this question, we have the leading term, leading coefficient and the degree of the given polynomial. The leading term, leading coefficient and degree will depend on the highest power of the variable and hence we write the solution for the given question.

Complete step by step solution:
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations. The constant term will be numerical form and the variables are in the form of alphabetical form.
In a polynomial, the leading term is the term with the highest power of x.
Now consider the given polynomial, \[f(x) = 3{x^5} + 6{x^4} - x - 3\]. Here we have to see the highest power of the variable of the polynomial function.
Therefore, the leading term of the polynomial \[f(x) = 3{x^5} + 6{x^4} - x - 3\] is \[3{x^5}\]
The leading coefficient of a polynomial is the coefficient of the leading term.
Now consider the given polynomial, \[f(x) = 3{x^5} + 6{x^4} - x - 3\] . Here we have to see the coefficient of highest power of the variable of the polynomial function.
Therefore, the leading coefficient of the polynomial \[f(x) = 3{x^5} + 6{x^4} - x - 3\] is \[3\]
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
Now consider the given polynomial, \[f(x) = 3{x^5} + 6{x^4} - x - 3\] . Here we have to see the power of the highest power of the variable of the polynomial function.
Therefore, the degree of the polynomial \[f(x) = 3{x^5} + 6{x^4} - x - 3\] is \[5\]
Hence the leading term, leading coefficient, and degree of this polynomial \[f(x) = 3{x^5} + 6{x^4} - x - 3\] is \[3{x^5}\] , 3 and \[5\] respectively.

Note: To write the answer for this question the student must know the actual definition of the leading term, leading coefficient and degree of the given polynomial. These terms will depend on the given polynomial function. Hence definition is important for this concept.