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Factor completely.

x^2+4x-21

(x + 7) (x - 3)

Step-by-step explanation:

The constants in the binomial factors must multiply to give - 21 and must add to give + 4. Since you're familiar with your multiplication tables, you know that ...

-21 = - 1·21 = - 3·7 = - 7·3 = - 21·1

The sums of these factor pairs are 20, 4, - 4, - 20. Clearly the pair of choice is - 3 and 7. Then the binomial factors are ...

(x - 3) (x + 7)