What is a Leading Coefficient?

The boxed polynomial has three terms: 6x³, -4x², and 8x
A coefficient is the constant at the front of a term
Since we only have one variable, 'x', the degree of each term will be the exponent of 'x'
The term with the highest degree is 6x³, so the coefficient of that term is the leading coefficient
Example 'B' is not in standard form, but we can still pick out the leading coefficient
In example 'C', the constant 6 can be written as 6x⁰ which equals 6*(1)

1. A coefficient is the constant at the front of a term
1. In standard form, the terms of a polynomial are written in order from highest to lowest degree
2. So the coefficient of the highest degree will LEAD the expression
1. This polynomial has three terms: 5x³, -2x², and 3x
2. Since it's written in standard form, the leading term has the highest degree
3. 5x³ has a degree of 3
4. The coefficient of 5x³ is 5, so that is our leading coefficient
1. This polynomial has three terms: 8x², 4x³, and -7x
2. We could find the leading coefficient as the polynomial is written, but it's even easier if we rewrite it in standard form
3. The Commutative Property of Addition says we can add terms in any order
4. 4x³ has a degree of 3
5. The coefficient of 4x³ is 4, so that is our leading coefficient
1. This polynomial is a constant, so it only has one term: 6
2. Since x⁰=1, this constant can be written as 6x⁰
3. 6x⁰ has a degree of 0
4. The coefficient of 6x⁰ is 6
5. So for a constant, the leading coefficient is the constant!
1. This polynomial has two terms: -3x, and 5
2. Remember that the constant 5 is the same as 5x⁰, so this polynomial is written in standard form
3. -3x can be written as -3x¹, so it has a degree of 1
4. The coefficient of -3x is -3, so that is our leading coefficient

What is a leading coefficient?