How do you factor completely #x^2-x-72 #?

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Answer 1 · 2016-04-13T16:23:11

# color(blue)( (x + 8 ) ( x - 9) # is the factorised form of the expression.

#x^2 - x - 72#

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*(-72) = -72#

AND

#N_1 +N_2 = b = -1 #

After trying out a few numbers we get #N_1 = -9# and #N_2 =8#

#8*(-9) = -72#, and # 8+(-9)= -1#

#x^2 - x - 72 = x^2 - 9x + 8x - 72#

# = x ( x - 9) + 8 ( x - 9 ) #

#(x - 9 )# is a common factor to each of the terms

# = (x + 8 ) ( x - 9) #

# color(blue)( (x + 8 ) ( x - 9) # is the factorised form of the expression.