Question

x^4+2x^3+x+2=0

Answer 1

what do you need help with

Answer 2

factor x^3 in x^4+2x^3

Answer 3

x^3(x+2)+x+2=0
since x+2 is a common factor also factor it out

Answer 4

yeah I get x^3(x+2)+1(x+2)

Answer 5

yes now factor out x+2

Answer 6

Ok I get x+2=0 which is -2 and then I get x^3+1=0 and x^3=-1 and that's where I get stuck

Answer 7

so \[x=-2\] correct
\[x^3=-1 \implies x=\sqrt[3]{-1}=?\]

Answer 8

oh ok it would be + or - 1i right?

Answer 9

since we are having a cube the re are three numbers not -1 and -1 and -1
since -1*-1*-1=-1

Answer 10

so it would just be -1?

Answer 11

yes but it is clever to write all of them since this equation is to the power of 4 the roots are 4
(-2,-1,-1,-1)

Answer 12

OK that's where I didn't get it because I knew we were supposed to get 4 values of x but I only got 2. Thanks so much for your help!

Answer 13

yw