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How do you factor x^2-7?

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emmerrill | Student, Grade 11 | eNotes Newbie

Posted May 23, 2013 at 5:18 PM via web

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How do you factor x^2-7?

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 23, 2013 at 5:22 PM (Answer #1)

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Use the relation a^2 - b^2 = (a - b)(a + b)

`x^2 - 7`

= `x^2 - (sqrt 7)^2`

=> `(x - sqrt 7)(x + sqrt 7)`

It should be noted that x^2 - 7 does not have rational factors.

The expression `x^2 - 7 = (x - sqrt 7)(x + sqrt 7)`

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