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Factor x^2-6x-7

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3 Answers

 X^2 - 6X -7 =
 factor it into ( x - a) ( X-b) , in such a way that
   a+ b = 6
   ab = -7 
   a = 7 b= -1
    ( x -7 ) ( X +1) 

1) think of the last number as the PRODUCT of the polynomial.  Think of the factors that go into it (when there is no number in front of the x^2, ie the letter (a) in front of the x^2 = 1 (ax^2 +bx +c where a, b, and c are numbers). The only factors of 7 are (1 and 7).

2) the rest is figuring out positive/negative of the factors, if the (b) is negative and the (c) is positive, then both of the factors will have negative numbers (remember.

 (x+1) (x-7) will equal the FOIL (first, outside, inside, last). - the -7x +1x equals the -6x you need. 

The way to solve this is to ask yourself the question:

What two factors have a sum of -6 (the coef of the x term) and a product of -7 (the coef of the constant) ...

After a little thought you will realize that 1 * -7 = -7 and 1 + -7 = -6

... Let me know if you need any more help.