Question

Given the expression: 3x10 − 48x2

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

Part A: Rewrite the expression by factoring out the greatest common factor.

The expression can be factored as:

3x10 - 48x2 = 3x(10 - 16x) = 3x(-6x + 10)

Here, the greatest common factor is 3x, which can be factored out.

Part B: Factor the entire expression completely. Show the steps of your work.

Starting from the expression 3x(-6x + 10), we can factor it completely as:

3x(-6x + 10) = 3x(-6x + 5 + 5) = 3x(-6x + 5) + 3x(5)
= 3x(-6x + 5) + 15x = 3x(-2x + 5) + 15x
= -6x(2x - 5) + 15x = -6x(2x - 5) + 3(5x)
= -6x(2x - 5) + 3(5)x = -6x(2x - 5) + 15x

So, the expression 3x10 - 48x2 can be factored completely as:

3x10 - 48x2 = -6x(2x - 5) + 15x