Can #y=x^2-16x+64 # be factored? If so what are the factors ?

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Answer 1 · 2016-01-12T17:47:06

Yes the expression can be factorised.
# color(blue)((x-8) (x -8)# are the factors

#y = x^2 -16x +64#

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like #ax^2 + bx + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c =1*64 = 64#

AND

#N_1 +N_2 = b = -16#

After trying out a few numbers we get #N_1 = -8# and #N_2 =-8#
#-8*-8= 64#, and #(-8)+(-8)= -16#

# =x^2 -16x +64 = x^2 -8x -8x+64#

#= x(x -8) -8(x-8)#

# =color(blue)((x-8) (x -8)#