Question

(100pts)An expression is shown below: 2x3 + 10x2 − 4x2y − 20xy 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

Answer:

2x(x + 5)(x - 2y)

Step-by-step explanation:

Answer 2

Answer:

2x(x + 5)(x - 2y)

Step-by-step explanation:

a) 2x³ + 10x² - 4x²y - 20xy

The greatest factor among the expression is the greatest factor common to each term in the expression. From the expression, each of the terms has a factor of 2x, hence the greatest common factor is 2x, therefore:

2x³ + 10x² - 4x²y - 20xy = 2x(x² + 5x - 2xy - 10y)

b)  2x³ + 10x² - 4x²y - 20xy = 2x(x² + 5x - 2xy - 10y)

= 2x[x(x + 5) -2y(x + 5)]

= 2x(x - 2y)(x + 5)

= 2x(x + 5)(x - 2y)

2x³ + 10x² - 4x²y - 20xy = 2x(x + 5)(x - 2y)