Question #d5777

2 Answers
Dec 5, 2017

#x=-2,3#

Explanation:

Start off by organizing #-4x+24-4x^2# properly. Like this:
#-4x^2-4x+24#

I'd start off by doing the Slip and Slide method that was taught at my school. So, I'd multiply #-4# (from the #x^2#) and #24# together.

#-4x^2-4x+24#
to
#x^2-4x-96#

Notice how I put the product of #-4 * 24# into the last space of the equation. (the #-4# will come into play soon, so don't forget about it just yet!)

Now factor the equation! Two numbers that equal #-96# when multiplied and #-4# when added together are #8# and #-12#.

The equation for this would be from #x^2-4x-96# to this:

#(x+8)(x-12)#

Next, divide #8# and #-12# by #-4# (the one that we took out earlier and multiplied with #24#). The remaining answer should look like this:

#(x+2)(x-3)#

Therefore, #x=-2,3#

Dec 5, 2017

#(x-2)# and #(x+3)#

Explanation:

It is always easier to start by rewriting the expression in standard form.

# - 4x +24-4x^2 #

# -4x^2-4x+24#

Now to find the factors, we must factor. The first step is to set the expression equal to #0# to make it an equation.

#-4x^2-4x+24=0#

It is easier if the coefficient of #x^2# is not a pesky negative. We can simplify by dividing both sides of the equation by #-4#.

#x^2+x-6=0#

From here we use the technique where we must find #2# numbers that equal #c# in the expression #ax^2+bx+c# that will also add up to equal to #b#.

Two numbers that satisfy this are #-2# and #3#.

We can check:

#(-2)(3) = -6#
#(-2) + (3) = 1#

Now we just break up #x^2+x-6# using the numbers we just found.

#(x-2)(x+3)=0#

So the factors of # - 4x +24-4x^2 # are #(x-2)# and #(x+3)#.