Factor out the greatest common factor from the expression 36x^3-30x^2

To factor out the greatest common factor from the expression 36x^3 - 30x^2, we need to find the largest number or variable that divides evenly into both terms.

First, let's look at the numbers 36 and 30. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The largest number that divides evenly into both 36 and 30 is 6.

Next, we look at the variables x^3 and x^2. Both terms have x raised to a power, so we can factor out x^2 as the largest common variable.

Therefore, the greatest common factor of 36x^3 and 30x^2 is 6x^2.

Factoring out 6x^2 from the expression, we get:
36x^3 - 30x^2 = 6x^2(6x - 5)

So, the factored form of the expression is 6x^2(6x - 5).

To factor out the greatest common factor from the expression 36x^3 - 30x^2, we need to find the largest common factor of the coefficients (36 and 30) and the variable factors (x^3 and x^2).

Step 1: Find the greatest common factor of the coefficients.
In this case, the greatest common factor of 36 and 30 is 6.

Step 2: Find the greatest common factor of the variable factors.
The variable factors are x^3 and x^2. The greatest common factor here is x^2, as it is the highest power of x that both terms have.

Step 3: Factor out the greatest common factor.
Now, we can factor out the greatest common factor from both terms. The greatest common factor is 6x^2.

The factored expression is:
6x^2(6x - 5)

36x^3 - 30x^2.

6x^2(6x - 5).