How to Find the Leading Coefficient of a Polynomial?

The leading coefficient of a polynomial is the coefficient of the term with the highest degree (highest exponent).

Here's a breakdown of how to find it:

1. Identify the Degree of the Polynomial

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 3x^4 + 2x^2 - x + 5, the degree is 4 because x^4 is the highest power of x.

2. Find the Term with the Highest Degree

Locate the term in the polynomial that contains the variable raised to the highest power (the degree you identified in step 1). In the example above, the term with the highest degree is 3x^4.

3. Identify the Coefficient of That Term

The leading coefficient is the number that is multiplied by the variable in the term with the highest degree. In the term 3x^4, the coefficient is 3. Therefore, the leading coefficient of the polynomial 3x^4 + 2x^2 - x + 5 is 3.

Examples

Polynomial: 7x^2 + 4x - 1
- Degree: 2
- Term with highest degree: 7x^2
- Leading Coefficient: 7
Polynomial: -5x^5 + x^3 - 8
- Degree: 5
- Term with highest degree: -5x^5
- Leading Coefficient: -5
Polynomial: x - 2 (which can also be written as 1x - 2)
- Degree: 1
- Term with highest degree: x (or 1x)
- Leading Coefficient: 1
Polynomial: 9 (which can also be written as 9x^0)
- Degree: 0
- Term with highest degree: 9 (or 9x^0)
- Leading Coefficient: 9

Important Notes

Make sure the polynomial is written in standard form (terms arranged in descending order of their degrees) to easily identify the term with the highest degree. If it's not, rearrange the terms first.
The leading coefficient can be positive, negative, or zero (although if it's zero, the term wouldn't typically be written, and the degree would be lower).

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