# How can you factor out x^2+x+1 ?

Relevance

The factors you require need to add together to make 1 and multiply together to equal 1, this is a hard problem though and if we run the coefficients through the determinant (b^2 - 4ac) we get a negative value which means we will need to use imaginary numbers. It is a lot easier in this case to use the quadratic formula but I will factor it out by making a perfect square as you asked for it to be factorised.

(x+1/2)^2+1/2=0

(x+1/2)^2=-1/2

(x+1/2) = +/- sqrt(-1/2)

(x+1/2)= +/- i.sqrt(1/2)

x = -1/2 +/- i.sqrt(1/2)

Where i is the square root of -1 or the imaginary number

NOTE: The above answers that say (x+1)^2 is a factor of this equation are WRONG. (x+1)^2 factors out to be x^2 + 2x + 1 and hence the b term is 1x greater than you want. Just a word of warning...

• Anonymous

(x+1)(x+1)

or

(x+1)^2

• Anonymous

okay so i had an answers and then i read VVV guys answer and he's write. i totally screwed up. (x=)^2 is wrong. cuz the 1 and 1 equals 2x, not one x. my mistake. haha.

That is not factorable!