Question

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

Answer 1

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

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`