How do you factor #x^2-2x-80#?

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Answer 1 · 2016-03-10T15:57:32

# color(blue)( (x + 8 ) (x -10) # is the factorised form of the expression.

#x^2 -2x -80#

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*(-80) = -80#

AND

#N_1 +N_2 = b = -2#

After trying out a few numbers we get #N_1 = -10# and #N_2 =8#
#8*(-10) = -80#, and #8+(-10)= -2#

#x^2 -2x -80 =x^2 -10x +8x -80 #

# = x(x -10) +8 (x -10) #

# =color(blue)( (x + 8 ) (x -10) #