How do you factor #x^2 - 10x + 24#?

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Answer 1 · 2015-05-03T12:11:35

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*24 = 24#
AND
#N_1 +N_2 = b = -10#

After trying out a few numbers we get #N_1 = -6# and #N_2 =-4#

#-6*-4 = 24#, and #(-6)+(-4)= -10#

#x^2 - 10x + 24 = x^2 - 6x - 4x +24#

# = x(x-6) - 4(x - 6)#

#(x - 6)# is a common factor to each of the terms

# = color(green)((x-6)(x-4)#