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How do I factor this polynomial k^2 + k - 42 / 1 - k

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1 Answer

(k+a)(k+b) = k2 + ak + bk + ab = k2 + (a+b)k + ab
                                                                      ↓            ↓
             .                                                        1          -42
  7 – 6 = 1 and  7 * (-6) = -42
 k2 + k - 42 = (k - 6)(k + 7) 
2.                                                                   ↓            ↓
                                                                     -1          -30
-6*5 = -30 and -6 + 5 = -1 
k2 - k - 30 = (k - 6)(k + 5)