Question

What is the leading term, leading coefficient and degree of this polynomial $ - 2{x} - 3{x^2} - 4{x^4} + 3{x^6} + 7$?

Answer 1

Hint: Read the question carefully, and rearrange the given terms in descending order of powers. The leading term means first term and the leading coefficient means the coefficient means the coefficient terms. The degree of the polynomial means the highest degree of polynomial.

Complete step-by-step solution:
The given polynomial is
$ - 2{x} - 3{x^2} - 4{x^4} + 3{x^6} + 7$.
Rearrange the terms in descending of powers (higher to lower),
After arranging the terms higher degree to left degree we have,
$3{x^6}- 4{x^4}-3{x^2}-2{x}+7$ ,
Here, we have to find the leading term in this polynomial.
Leading term means the first term of polynomial.
Therefore here the leading term is $3{x^6}$.
Leading coefficient means the, coefficient of the leading term, here in the polynomial, we have
The leading coefficient is $3$.
And then we have to find the value of the degree of this polynomial.
Therefore the degree of the polynomial is $6$.
Because the highest power (degree) is $6$.
Therefore the leading form is $3{x^6}$
The leading coefficient is $3$.
Degree of polynomial is $6$.

Note: The highest power of the variable that occurs in the polynomial is called the degree of a polynomial. The leading terms are the term with the highest power, and its coefficient is called the leading co – efficient.
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial’s monomials (individual terms) with non-zero co – efficient. 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.