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The factor theorem states that a polynomial f(x) has a factor (x − k) if and only if f(k) = 0
f(x) = x^2+7^x+12=0 |As Stated in the Question
factoring
(x+4)(x+3) = 0 Note:SUM of the inner product(4x) and the outer product(3x) = 7x
(x+4)=0
x = -4
(x+3) = 0
x = -3
Solution Set for x is: -4,-3