Question

An expression is shown below:

4m3 + 12xm2 − 8m2 − 24xm

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

Part B: Factor the entire expression completely. Show the steps of your work. (6 points)

Answer 1

a) The polynomic expression is 4 · m · (m² + 3 · x · m - 2 · m - 6 · x).

b) The polynomic expression is 4 · m · (m - 2) · (m + 3 · x).

How to factor a polynomic equation by algebraic procedures

a) In this problem we need to rewrite the expression by the extracting the factor common to the four monomials that are part of the polynomial. Now we proceed to present the procedure in detail:

4 · m³ + 12 · x · m² - 8 · m² - 24 · x · m            Given

4 · (m³ + 3 · x · m² - 2 · m² - 6 · x · m)             Distributive and associative properties / (- a) · b = - a · b

4 · m · (m² + 3 · x · m - 2 · m - 6 · x)                Result

b) And now we factor the entire expression completely by algebraic means:

4 · m · (m² + 3 · x · m - 2 · m - 6 · x)                Given

4 · m · [m · (m + 3 · x) - 2 · (m + 3 · x)]             Distributive and associative properties / (- a) · b = - a · b

4 · m · (m - 2) · (m + 3 · x)                                Distributive and associative properties / (- a) · b = - a · b / Result

To learn more on polynomials: https://brainly.com/question/20121808

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