Question

how do I solve the polynomial equation x^3+5x=9x

Answer 1

First you want to always set a polynomial equation equal to 0, so the best move first is to subtract 9x from both sides:
x^3+5x=9x turns into x^3-4x=0
Now we can forget about the 0 for a bit and focus on x^3-4x.
Now these both share one solitary x so we can simply factor this out giving us:
x(x^2-4)
At this point it is solved as a difference of squares. Would you like for me to explain this too?

Answer 2

yes

Answer 3

would that turn into x(x-2) (x-2) ?

Answer 4

A difference of squares will always have opposite signs between the binomials, so flip one of the negative signs and you have it!

Answer 5

If you want to, you can always check yourself by multiplying out of the FOIL method the O and I. If these two terms cancel each other out, the difference of squares was achieved correctly.

Answer 6

so, then it would be x(x+2) (x-2) ?

Answer 7

Oh, okay. Thanks

Answer 8

Yes it would

Answer 9

thanks

Answer 10

can you help with a different equation too? x(x+8)=x^2+6x+9 ? I know that first you have to equal it to zero, but after I equal it to zero I am left with 2x+9 and I don't know what to do next.

Answer 11

@flixoe