how to factor this quadratic equation step by step

Question

x² -10x-24

Answer 1

Hi Britt,

 

You have two numbers that adds/subtracts up -10 and multiplies up -24.  By looking at "C" term (from Ax² + Bx + C), C is negative which means one of them must be negative.  To figure which one is negative, look at the "B" value which is -10 and that will tell you bigger number of the two will be negative.

 

So, let find out what makes 10 and 24.  Let's start from the middle:

 

6 and 4.  It makes 10 and 24 but the signs must be the same for both.  This two pairs will give +10 or -10 for "B" value and +24 for C value.  If C is -24 by using 6 & 4, the middle term will be either +2 or -2.  So this will not work.

 

8 and 3.  You can tell right from the start that these two numbers do not make 10.  So, this will not work.

 

12 and 2.  It makes 10 when they subtract and they multiplies to 24.  But which one is positive and which one is negative? the bigger one is negative since middle term is negative: 12 (-12+2 = -10) & (-12)(+2) = -24.  So, it turns out like this:

 

(x-12) (x+2)

 

If you have gone through quadratic formula, you can use that to get those answers as well.  Good luck.

 

If you have a questions you want me to look at, send me the message (click my name).  I will give you all the details you need.