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Degree and Leading Coefficient/Term

This Calculator computes the degree, leading coefficient and leading term of a given Polynomial.

How to use this calculator?

Variable Input a single-letter that is the polynomial variable. Examples :
polynomial = 4x+1 , then input variable = 'x'
polynomial = 9t + 5 , then input variable ='t'
Polynomial Are accepted :
  • The Polynomial variable
  • Polynomial coefficients : must be rational numbers e.g. integer numbers (-4) or fractions (1/4) or decimals (3.6).
  • Operators : + - * / ^ (the last is the power operator so x^2 = `x^2`)
  • Parentheses : an example of use is (x^2+1)(x-5)
Examples Polynomial = x^2-4x+1 (variable = 'x')
Polynomial = (x^2-1)(x-5)-3 (variable = 'x')
Polynomial = x^3-4/3*x^2+1 (variable = 'x')
Polynomial = 0.23*t^2-1/5*t+1/2 (variable = 't')

What are the leading term, leading coefficient and degree of a polynomial ?

  • The leading term is the polynomial term with the highest degree.
  • The degree of a polynomial is the degree of its leading term.
  • The leading coefficient is the coefficient of the leading term.

So we can write,

`\text{Leading term} = \text{Leading coefficient}^\text{Degree}`

Usually, the leading term of the polynomial is written first. So, the general expression of a polynomial is,

`P(x) = a_n*x^n + a_(n-1)*x^(n-1)+ ... + a_2*x^2 + a_1*x + a_0`

The leading term is `a_n*x^n` which is the term with the highest exponent in the polynomial.

The degree of the polynomial is the degree of the leading term (`a_n*x^n`) which is n.

The leading coefficient is the coefficient of the leading term. So, it is equal to `a_n`.

Examples

P(x) = `2x^3+x+4`
Leading term = `2x^3`
Leading coefficient = 2
Degree = 3

P(x) = `-x^5+x^4+2x^3-1`
Leading term = `-x^5`
Leading coefficient = -1
Degree = 5

P(x) = `x^2-1`
Leading term = `x^2`
Leading coefficient = 1
Degree = 2

See also

Polynomial calculators
Math Calculators