explain x^2+4x-x-4 step by step please

Question

How do I get the answer (x+4) (x-1), from x^2+4x-x-4? Please explain step by step. sharon

Answer 1

First you must combine like terms. In this case 4x and -x can be added together to make 3x.
Next you must factor the polynomial. So you can either 1) use guess and check or 2) use the AC method. 
The AC method is the easiest to list. So first list the factors of a x c (a being x² and b being -4). After that you must list the factors of the result (-4).
1 and -4
2 and -2
-1 and -4
From your list pick the two factors that add up to your b term (-3). This happens to be -4 and 1. Lastly set x equal to the number and solve for x - C - C being one of your solutions.

x = -4             x = 1

+4  +4           +1   +1

x + 4 = 0        x + 1 = 0
Put your answers in parenthesis to create two binomials multiplied together and you have your answer                 

(x+4)(x-1)

Answer 2

Each, out of two groups (x²    +    4x)  and (-x      -   4) has a common factors
                                    ↑   and    ↑            ↑   and   ↑  
                                 x · x      4 · x         -1 · x   -1 · 4  

Let's factor them out: x(x + 4) - 1(x + 4)  ---> (x + 4)(x - 1) <--- the final answer
                                      ↑             ↑
                                    common factor out