Find all real and imaginary solutions to the polynomial equations by factoring and /or using quadratic formula

Question

X^3+6=-2 solve this using instruction 

Answer 1

All higher level equations are solved by bringing all the terms on one side, zero on the other side, and then factoring. So we have

 

x³+8=0     This is the sum of perfect cubes, which can be factored as follows

(x+2)(x²-2x+4)=0

So one answer is x+2=0 or x=-2.

 

The other answers can be solved for using the quadratic formula on x²-2x+4=0.

 

Those answers come out to be (2+√-12)/2 and (2-√-12)/2. These simplify down to 1+i√3 and 1-i√3.

 

Hope this helped.