You are given the expression 36x4y3 − 16x3y. Part A: Find a common factor for the expression that has a coefficient other than 1 and that contains at least one variable. (1 point) Part B: Explain how you found the common factor. (1 point) Part C: Rewrite the expression using the common factor you found in Part A. Show every step of your work. (2 points)

B. The common factor was found from the multiplication of the greatest common factor of the numeric exponents and the smallest exponent of each variable.

C. The factored expression with the common factor is: 4x³y(9xy² - 4).

How to find the common factor of a polynomial expression?

To find the common factor of a polynomial expression, we have to:

Find the greatest common multiple of the numeric coefficients.

Select the smallest exponent of each variable.

Then, these terms are multiplied.

In this problem, the expression is given as follows:

36x^4y³ - 16x³y

Hence the lcm and the smallest exponents are given as follows:

The least common multiple of the numeric coefficients 36 and -16 is of 4.

The smallest exponent of x is of 3.

The smallest exponent of y is of 1.

Hence the least common factor of the expression is given as follows:

4x³y.

The expression is factored placing the common factor in evidence and then dividing each term by the common factor, hence:

36x^4y³/4x³y = 9xy².

16x³y/4x²y = 4.

Then the simplified expression is:

4x³y(9xy² - 4).

More can be learned about common factor factoring at https://brainly.com/question/28930715

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