3x^3-27x^2+60x factor completely?

Question

If you could show me how you got the answer.

Answer 1

first take out any # or letter u can out:

3 and x!

3x(x^2 - 9x + 20)

now u can factor the parenthesis:

3x(x +/- _)(x +/- _)

u have to find two numbers that multiply together to be +20, and add-subtract each other to get -9

so try out some numbers: (1, 20). (2, 10). (4, 5)
see how 4 and 5 can add up to 9, and multiply to be 20!

3x(x - 4)(x-5)

(it is x-4 and x-5 because they have to add up to -9, and multiply eachother to be +20). let's check our answer:

3x(x^2-4x-5x+20)
3x(x^2-9x+20) check!! :)

Answer 2

3x^3-27x^2+60x
= x(3*x^2 - 27x + 60)
Now,
(3*x^2 - 27x + 60)
= 3*x^2 - 15x - 12x + 60
= 3x(x-5) - 12(x-5)
= (x-5)(3x-12)
= 3(x-4)(x-5)

Hence, the expression 3x^3-27x^2+60x factors completely and the required factorisation is:
3x(x-4)(x-5).

Answer 3

3x(x^2-9x+20)
3x(x-4)(x-5)