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Factor x^2-6x-7

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
 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) 
Beth L. | Patient, Knowledgeable and Very Qualified Mathematics TutorPatient, Knowledgeable and Very Qualifie...

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. 

Joseph B. | Texas Certified Math and Science TeacherTexas Certified Math and Science Teacher
5.0 5.0 (1172 lesson ratings) (1172)

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.