Question

WILL MEDAL!!
Please help!
Find the real or imaginary solutions of each equation using factoring.
x^3 + 2x^2+5x+10=0
x^4-10x^2=-9

Answer 1

i fancy this one, for sure
\[x^4-10x^2=-9\]

think: \(z = x^2\)

Answer 2

the first one notice that you can recollect (group) and factor

Answer 3

and the second is as @IrishBoy123 mentioned think of x^2 as another variable z

Answer 4

so in other words you will just get a quadratic equation which is nicer to deal with

Answer 5

so you're saying do z^2 + 10z

Answer 6

@xapproachesinfinity ^^

Answer 7

close but not quite
\[z^2-10z=-9 \Longrightarrow z^2-10z+9=0 \]

Answer 8

Ok thank you! Do you know how to do the first one?

Answer 9

so now you are trying to solve \[z^2-10z+9=0\] for z
once you found z return back to x

Answer 10

the first is really straight forward
\[x^3 + 2x^2+5x+10=0 \Longrightarrow (x^3+2x^2)+(5x+10)=0\]
\[x^2(x+2)+5(x+2)=0 \Longrightarrow (x^2+5)(x+2)=0 \]

Answer 11

Thank you! :)

Answer 12

welcome