Question

Factor x2 - 2x + 3

Answer 1

Do you mean Factor x^2 - 2x + 3

Answer 2

@aric200 yes that's got to be the equation

Answer 3

anyway , to factor we focus on the middle term and the last term first
then the sign patterns of the equation

Answer 4

@aric200 yes sir

Answer 5

so the last term we have is a 3 and there is only one combination
which is
1 x 3 = 3

so now let's grab the middle term. We notice that there is a -2
so our 1 must be positive and our 3 must be negative
1-3 = -2

Answer 6

It bothers me when people do not put the ^Carrots.

Answer 7

or am I reading this too fast?
wait... I'm using discriminant formula

Answer 8

(-2)^2-4(1)(3)
4-12 = -8 oh nice.. we can't factor this -_-
quadratic formula time

Answer 9

\[\frac{-b \pm \sqrt{b^2-4ac} }{2a} \]

Answer 10

so with the discriminant formula we already figured out the square root portion which was -8, so we let a = 1 b = -2 and c = 3
because our equation \[x^2-2x+3\] in the form of the standard quadratic equation which is \[ax^2+bx+c\]

Answer 11

now we just plug in our data
\[\frac{2 \pm \sqrt{-8} }{2}\]

Answer 12

but we are not done... we can split that 8 up and negatives aren't allowed in the radicals which means we are going to get an imaginary or i out of this

Answer 13

\[\frac{2 \pm 2\sqrt{2}i }{2}\]

Answer 14

now we can get split this up and get rid of the 2's

Answer 15

\[\frac{2+2 \sqrt{2}i}{2}, \frac{2-2 \sqrt{2}i}{2}\]

Answer 16

\[1+\sqrt{2}i, 1-\sqrt{2}i\]

Answer 17

which is our roots..

Answer 18

@UsukiDoll so thats it?!

Answer 19

I think it should look like this?
not sure
\[(x-(1+\sqrt{2}i))(x-(1-\sqrt{2}i) )\]

Answer 20

@ganeshie8 I'm missing something in here...aren't I?

Answer 21

it's just that when I use to do those problems, all of my professors care about are the roots and I didn't have to put it back into factored form like what I just typed.

Answer 22

yeah the given quadratic cannot be factored over integers, it is prime