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Im having trouble factoring 25x^2-10x+1 using the ac method. I end up with (5x-5)(5x-5)

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2 Answers

 Have to choose 2 numbers whose some equals -10, and product 25
 
   How about -5, -5    a+b = -10
                                a.b = 25     So the factors are 
 
 
      -10X = -5X - 5X
 
    25 X2 - 5X -5X +1 =
   5X ( 5X-1 )  - ( 5X -1) =
    (5X -1 ) ( 5X - 1) = 25X2 - 10X +1
 
    You should be good in the quadratic expression: 
   
     From ( a ±b )= a2±2ab + b2    and  recognize this immediately.
 
 
 
 
 
 
 

(a ± b) = a2 ± 2ab + b2
~~~~~~~~~~~~
25x2 - 10x + 1 = (5x)2 - 2· 5x · 1 + 12 = (5x - 1)2 

In general:
ax2 + bx + c = a(x - x1)(x - x2) , x1 and x2 are roots of equation ax2 + bx + c = 0 , and
x12 = (-b ± √D)/2a , D = b2 - 4ac .
~~~~~~~~~~~~
25x2 - 10x + 1 = 0
D = (-10)2 - 4 · 25 · 1 = 100 - 100 = 0
the equation has only one root (actually 2 roots with the same value) 
x12 = -(-10)/(2 · 25)
x12 = 1/5
25(x - 1/5)(x - 1/5) = (5x - 1)(5x - 1) = (5x - 1)2