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

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

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Aaron G. | A Personal Touch: AP Classes, ACT, SAT And Much MoreA Personal Touch: AP Classes, ACT, SAT A...
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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)

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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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