Question

An expression is shown below:

10n3 − 15n2 + 20xn2 − 30xn

Part A: Rewrite the expression so the GCF is factored completely. (4 points)

Part B: Rewrite the expression completely factored. Show the steps of your work.

Answer 1

An expression is shown below:

10n³− 15n² + 20xn² − 30xn

Part A: Rewrite the expression so the GCF is factored completely. (4 points)

10n³− 15n² + 20xn² − 30xn

2*5*n*n*n-5*3*n*n+2*5*2*x*n*n-2*5*3*x*n

Greatest common factor=5*n=5n

Part B: Rewrite the expression completely factored. Show the steps of your work.

Solution given;

10n³− 15n² + 20xn² − 30xn

5n(2n²-3n+4xn-6x)

5n(2n²+4xn-3n-6x)

5n(2n(n+2x)-3(n+2x))

5n(n+2x)(2n-3)

Answer 2

`5n(2n-3)(n+2x)`

Explanation:

Step 1: Rewrite the expression so the GCF is factored completely

`10n^(3) - 15n^(2) + 20xn^(2) - 30xn`

The GCF is 5n so factor it out

`5n(2n^(2) - 3n + 4xn - 6x)`

Step 2: Rewrite the expression completely factored

`5n(2n^(2) - 3n + 4xn - 6x)`

`5n(2n(n+2x)-3(n+2x))`

`5n(2n-3)(n+2x)`

Answer:
`5n(2n-3)(n+2x)`