What are literal coefficient and numerical coefficient?

Example 1.

What is the literal coefficient and numerical coefficient of 8a?

Solution:

8a = 8 * a

The literal coefficient of the 8a is (a) and the numerical coefficient is 8.

See Definition of numerical coefficients.

See Definition of literal coefficients.

Example 2.

What is the literal coefficient and numerical coefficient of 24ab/8?

Solution:

24ab/8 =

(24/8) * (ab) =

3 * (ab)

(24/8) * (ab) =

3 * (ab)

The literal coefficient of the (24ab/8) is (ab) and the numerical coefficient is 3.

Example 3.

What is the literal coefficient and numerical coefficient of (-15x)?

Solution:

-15x = (-15) * x

The literal coefficient of the (-15x) is (x) and the numerical coefficient is (-15).

Example 4.

What is the literal coefficient and numerical coefficient of y^{45}?

Solution:

y^{45} =

1 * y^{45}

1 * y

The literal coefficient of the (y^{45}) is y^{45} and the numerical coefficient is (1).

Example 5.

What is the literal coefficient of 34y^{4}y?

Solution:

34y^{4}y =

34 * y^{4 + 1} =

34 * y^{5}

34 * y

34 * y

The literal coefficient of the (34y^{4}y) is y^{5} and the numerical coefficient is (34).