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how to find the leading coefficient of a polynomial?

Sagot :

A polynomial is represented as [tex]\mathbf{ax^n + bx^{n-1} + cx^{n-2} + .... + d}[/tex]

The leading coefficient of the polynomial is "a"

The leading coefficient of a polynomial is simply the coefficient of the variable with the highest power.

Take for instance:

[tex]\mathbf{2x^3 + 4x^2 + 5x - 6}[/tex]

In the above polynomial,

  • The highest power is 3
  • The variable is x
  • The coefficient of x is 2, when the highest power is 3

This means that, the leading coefficient is 2

Another instance:

[tex]\mathbf{-6y^5 + 2y^4 + 19y^3 - y^2 -17y + 1}[/tex]

In the above polynomial,

  • The highest power is 5
  • The variable is y
  • The coefficient of y is -6, when the highest power is 5

This means that, the leading coefficient is -6

In general,

The leading coefficient of the polynomial [tex]\mathbf{ax^n + bx^{n-1} + cx^{n-2} + .... + d}[/tex] is "a"

Read more about leading coefficients at:

https://brainly.com/question/15323309