An expression is shown below:

10n3 − 15n2 + 20xn2 − 30xn

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

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

Question

An expression is shown below:

10n3 − 15n2 + 20xn2 − 30xn

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

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

Aratox · Answer

Part A: 
The greatest common factor of the expression is 5n.

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

Part B:
To factor the expression completely, we need to look for common factors in each pair of terms.

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

Therefore, the completely factored expression is 5n(n + 5x)(2n - 3).

D14610 · Answer

@aratox wrote:

Part A: The greatest common factor of the expression is 5n. 5n(2n^2 - 3n + 4x^2 - 6x) Part B: To factor the expression completely, we need to look for common factors in each pair of terms. 5n(2n^2 - 3n) + 5n(4x^2 - 6x) 5n(n(2n - 3) + 5x(2x - 3)) 5n(n + 5x)(2n - 3) Therefore, the completely factored expression is 5n(n + 5x)(2n - 3).

thanks goat

Aratox · Answer

@d14610 wrote:

@aratox wrote:

Part A: The greatest common factor of the expression is 5n. 5n(2n^2 - 3n + 4x^2 - 6x) Part B: To factor the expression completely, we need to look for common factors in each pair of terms. 5n(2n^2 - 3n) + 5n(4x^2 - 6x) 5n(n(2n - 3) + 5x(2x - 3)) 5n(n + 5x)(2n - 3) Therefore, the completely factored expression is 5n(n + 5x)(2n - 3).

thanks goat

No problem, talk to me in DMs if you need any more help

D14610 · Answer

@aratox wrote:

@d14610 wrote:

i got 2 more questions like this if you could help i'd appreciate it big time

@aratox wrote:

Part A: The greatest common factor of the expression is 5n. 5n(2n^2 - 3n + 4x^2 - 6x) Part B: To factor the expression completely, we need to look for common factors in each pair of terms. 5n(2n^2 - 3n) + 5n(4x^2 - 6x) 5n(n(2n - 3) + 5x(2x - 3)) 5n(n + 5x)(2n - 3) Therefore, the completely factored expression is 5n(n + 5x)(2n - 3).

thanks goat

No problem, talk to me in DMs if you need any more help