How do you factor #c^3 - 2c^2 - 8c#?
The factorization of
begin by factoring out the variable
Next, factor the tri-nomial
by finding the factor of 8 that will subtract to get 2.
1 and 8 2 and 4
Since the second sign of the tri-nomial is subtraction the factors must have different signs.
Now factor the tri-nomial into two binomials.
Now complete the factors.
Here is a video on factoring.
Your starting expression looks like this
#c^3 - 2c^2 - 8c#
Notice that you can use
#c * (c^2 - 2c - 8)#
Now focus on the paranthesis. Notice that you can rewrite that expression as
#c^2 - 2c - 8 = c^2 +2c - 4c - 8#
#=c * (c+2) * (-4) * (c + 2)#
#= (c + 2) * (c - 4)#
The expression can thus be factored as
#c^3 - 2c^2 - 8c = color(green)(c * (c+2) * (c-4))#