How do you factor #2x^3-30x^2+100x# completely?

Question

809 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-16T22:58:08

#f(x) = 2x(x - 5)(x - 10)#

#f(x) = 2x(y) = 2x(x^2 - 15x + 50)#
Factor #y = x^2 - 15x + 50#.

Find 2 numbers knowing sum #(b = -15)#, and product #(c = 50)#.
They are #-5 and - 10#

#y = (x - 5)(x - 10)#

#f(x) = 2x(x - 5)(x - 10)#

Answer 2 · 2017-07-16T23:01:55

#2x(x-5)(x-10)#.

To factor a polynomial, look for the common factor in each term.

In the polynomial #2x^3-30x^2+100x#, each term has #2x#.

So you take out (divide) #2x# from each term.

That leaves you with #x^2-15x+50#.

You get #2x(x^2-15x+50)#. But it is still not fully factored.

#x^2-15x+50# can be factored to #(x-10)(x-5)#.

The answer is #2x(x-5)(x-10)#.