Question

Hello, can someone please explain me how to solve quadratics by factoring. I can't seem to get the right answer with this one;
x^2 - 2x + 1 = 0
So this is how I solved it but its wrong;
=(x-1)(x+1)
=x-1 +1=0 +1
x=1

=x+1 -1=0 -1
x = -1
Apparently, the answer is supposed to be two positive ones and I'm getting a positive and a negative one T-T PLEASE HALP.
PS: I really have no idea when its supposed to be a negative or a positive in the factoring process.

Answer 1

\[\huge\rm ax^2+bx+C=0\]
when the leading coefficient is 1
find two numbers when you multiply them you should get product of `AC` (a =leading coefficient , c=constant term)
and when you add/subtract them you should get middle term which is `b` (coefficient of x term)

check your answer (x-1)(x+1)
is -1 *1= C ??
-1+1 = b ??

Answer 2

correction
-1 *1= A C ??
-1+1 = b ??
what two numbers would you multiply to get `1` but when you add same numbers you should get `-2`

Answer 3

-1 :o?

Answer 4

like -1 x -1 = 1
and -1 + -1 = -2 ?

Answer 5

yes right
so it should be (x-1)(x-1 ) correcto ??

Answer 6

yuuus. BUT WAIT, thats the answer I got when I solved it with the formula, but when I did it by factoring i got +1 and -1 AND the answer sheet says its only +1 and +1.
IM CONFUSED.

Answer 7

(x+1)(x-1)
isn't correct
Because
-1 times 1 isn't equal to +1
-1+1 isn't equal to -2

Answer 8

the two numbers that will give you the product of AC and sum o b
are -1 and -1

Answer 9

and when Im factoring the original quadratic which is x^2 -2x + 1 = 0
How do I know if its positive or negative? T-T
BTW does your shortcut method work 100% with harder quadratics too ?

Answer 10

yes it always work if the leading coefficient is one
its known as headphone method
okay
how would you factor this x^2-2x+1= 0???