How do you factor completely: #8x^2 - 8x - 16#?

1 Answer

Answer:

#color(blue)(8(x+1)(x−2) #

Explanation:

#8x^2−8x−16#

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 = 8*(-16) = -128#
and
#N_1 +N_2 = b = -8#

After trying out a few numbers we get #N_1 = -16# and #N_2 =8#

#(-16)*8 = -128#, and #-16+8=-8#

#8x^2−color(blue)(8x)−16 = 8x^2−color(blue)(16x +8x)−16#

#= 8x(x−2) +8(x−2)#

#=(8x+8)(x-2)#

#= color(blue)(8(x+1)(x−2) # ,which is the factorised form.