+223 x6 + 729 does not have any real factors. You know this because if you move 729 to the other side of the equation you get: ----> x6 = -729 And you cannot take the sixth root (or any even numbered root) of a negative number.
If the problem wants you to use imaginary numbers then comment, and I'll give it a shot.
+223 Okay so what you are going to want to do is move the 729 to the other side of the problem as I showed above to get:
x6 = -729
Now since you only deal with complex (imaginary) numbers when you take the square root of a negative number, we are going to have to change this equation so we can take the square root of what is on the right side.
That means we need to change the x6 to an x2 and to do that you have to take the cubed (third) root. The cubed root of x6 is x2 since 2 goes into 6 three times.
Now we need to take the cubed root of -729 as well which equals -9.
So now we have ----> x2 = -9
Now we can take the square root of both sides to get:
x = plus or minus sqrt(-9) ----> (Remember when you take the square root of something it can be either plus or minus)
Now when you take the square root of a negative number, you do the same thing you do with a positive number but you just add an i.
So x = plus or minus 3i
So the factors of x6 are 3i and -3i
