how do you factor x^3-2x^2-25x+50?

Question

i know you factor by grouping but i got x^2(x-2)25(-x+2) can you go any further?

Answer 1

You have:

x²(x-2) + 25(-x+2)

Change the signs and use the distributive property, then finish with a difference of squares factorization:

x²(x-2) - 25(x-2)
(x² - 25)(x - 2)
(x + 5)(x - 5)(x - 2)

And we are done.

Answer 2

x^3 - 2x^2 - 25x + 50

x^2(x - 2) - 25(x - 2) {grouping}

(x^2 - 25)(x - 2)

(x + 5)(x - 5)(x - 2) {difference of two squares}

Answer 3

f(x) = x^3 - 2x^2 - 25x + 50

x^2(x - 2) - 25(x - 2)

=>(x - 2)(x^2 - 25)

now x^2 - 25 is in a^2 - b^2 form which equals (a+b)(a-b)

f(x) = (x-2)(x+5)(x-5)

Answer 4

(x^2 - 25)(x - 2) and (x^2 - 25) = (x+5)(x-5)

Answer 5

factor out -25

you get -25(x - 2)

then you get (x^2 - 25)(x-2)

which can be (x-5)(x+5)(x-2)

Answer 6

your answer is correct (except you forgot the - before the 25). thats as far as you can go

Answer 7

not being mean but I have no idea. I think the first person was the best