Question

i dont understand how to factor
x^4 + 4x^3 - 17x^2 + 48x + 60 ....
like... what are the steps...

Answer 1

--> (x^2 +ax + c)(x^2 +bx +d)
cd = 60
ad+bc = 48
c+d = -17
a+b = 4

Answer 2

are these cd.. ad+bc .. c+d.. and a+b just something i should remember when it comes to that factoring theory

Answer 3

not necessarily, it depends on the problem
there is no guarantee it will factor either, in this case when you try to solve the system you may get no solution

Answer 4

i see. i think i understand now. thank you

Answer 5

oh i messed up, it should be
c+d+ab = -17

sorry

Answer 6

factored out.. wouldnt it look like (x-1)(x+5)(x^2-12)

Answer 7

no not quite ... if you multiply that out you get
x^4 + 4x^3 -17x^2 -48x +60

Answer 8

thats what the equation is

Answer 9

Another way to try this problem is to guess some of the roots using the Rational Roots theorem. If you get lucky you might find one, which results in being able to reduce the degree of your polynomial by 1.

Answer 10

good point ^^
you could also graph it to find any roots that could be factored out

Answer 11

so if i am to solve this equation.. could i just leave the x values equal to + and - sqrt12

Answer 12

and 1 and -5

Answer 13

wait it looks like you had a typo in your original question...you put "+48x" but it should be "-48x" otherwise you don't get a nice answer

Answer 14

ahh . sorry about that.. . yes its -48x

Answer 15

in that case, you are correct
sqrt12 can be simplified to 2sqrt3 though

Answer 16

ok. ha. thanks again