Question

Find the real solutions of the equation by factoring.
x^3 + 6x^2 + 25x + 150 = 0
I know the answer is -6 but can someone explain the process?

Answer 1

I'll try my best! so...
\[x^3+6x^2+25x+150=0\]
When factoring cubic equations --> split it in half.
Factor the first two terms separately than the second two terms separately


\[x^2(x+6)+25(x+6)=0\]
---> combine

\[(x+6)(x^2+25)=0\]

Answer 2

what happened to the 150?

Answer 3

@sabrinathebruja factored (:
25(x+6) ---> 25x+150

Answer 4

so x3+6x2 became x2(x+6) and 25x+150 became 25(x+6) to make x2(x+6)+25(x+6) = 0?

Answer 5

@sunnnystrong

Answer 6

yep... when factoring cubics you need to make sure the factored term in the () is the same so you combine -->

\[(x^2+25)(x+6)\]

Answer 7

and they travel in conjugate pairs...

\(x = -6\)

and \( x =\pm i ~ 5\)

Answer 8

so how do i get -6? @sunnnystrong

Answer 9

@irishboy123 i is considered a real solution?

Answer 10

@IrishBoy123
thankk you!