How do you factor #15x^2 - 5x - 10#?

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Answer 1 · 2016-01-05T17:44:38

# =color(blue)( (15x+10)(x-1) #

#15x^2 -5x-10#

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 = 15*-10 = -150#
AND
#N_1 +N_2 = b = -5#

After trying out a few numbers we get #N_1 = -15# and #N_2 =10#
#10*-15 = -150#, and #10+(-15)= -5#

#15x^2 -5x-10 =15x^2 -15x +10x-10 #

# = 15x(x-1) +10 (x-1) #

#(x-1)# is a common factor to each of the terms

# =color(blue)( (15x+10)(x-1) #