Question

. Write the quadratic equation in factored form. Be sure to write the entire equation. x^2 - 5x - 24 = 0

Answer 1

Answer:

$(x+3)(x-8)=0$

Step-by-step explanation:

First, write out the equation as it is given in the problem:

$x^{2}-5x-24=0$

Now, you have to split up the "-5x" to get to factored form.  The way to do this is to look for the factors of "a" times "c" that sum to "b":

So, in this problem, a=1, b=-5, and c=-24.  So, find the factors of (1*-24) that sum to (-5). To clarify, (1*-24)=-24, so you have to find factorsof -24 that sum to -5.

Let's write out a list of factors.

$1,-24---1+-24=-23no\\-1,24---1+24=23no\\2,-12---2+-12=-10no\\-2,12----2+12=10no\\3,-8---3+-8=-5yes$

Therefore, our two factors will be 3x and -8x.

Now, let's rewrite our equation with these new factors in place of the -5x:

$x^{2}-5x-24=0\\x^{2}+3x-8x-24=0$

Next, find your factored expressions:

$x^{2}+3x-8x-24=0\\(x^{2}+3x)(-8x-24)=0$

Take the GCF from each set of parenthesis:

$x(x+3)-8(x+3)=0$

The GCFs that you took out will become your second in the set for factorde form.  It will be written as "x-8".

Therefore, your equation in factored form will be:

$(x+3)(x-8)=0$