how to factor x^2-x-20

Question

mathstudent55 · Answer

Since the coefficient of the x^2 term is 1, you need the following type of factoring: 
x^2 + ax + b 
1. Find two numbers that multiply to b and add to a. Let's call these numbers p and q. 
2. The factoring is simply (x + p)(x + q) 

In your case, if you compare x^2 - x - 20 to x^2 + ax + b, you have a = -1 and b = -20. 
You need two numbers that multiply to -20 and add to -1. 
What are two numbers that multiply to -20 and add to -1?

anonymous · Answer

$$x^2-x-20\x^2-4x+5x-20\x(x-4)+5(x-4)\(x-4)[x+5]\$$

mathstudent55 · Answer

@eninone
You wrote:
$x^2-x-20$
$x^2-4x+5x-20$
$x(x-4)+5(x-4)$
$(x-4)[x+5]$

Look at your second line:
$x^2-4x+5x-20$

If you add like terms, you get:
$x^2+x-20$

That is not the original polynomial.
You need -5x and + 4x, not -4x and + 5x.

anonymous · Answer

@mathstudent55 thanks, @kingban follow @mathstudent55