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To determine if \( x + 2 \) is a factor of \( x^2 + 7x - 9 \), we can use the factor theorem. According to this theorem, if \( x + 2 \) is a factor, then substituting \( x = -2 \) into the polynomial should yield zero. Plugging in, we get: \[ (-2)^2 + 7(-2) - 9 = 4 - 14 - 9 = -19 \] Since the result is not zero, \( x + 2 \) is not a factor of \( x^2 + 7x - 9 \). One might think they could just rely on polynomial division instead! Dividing \( x^2 + 7x - 9 \) by \( x + 2 \) reveals that you'll end up with a remainder. Always check your work to avoid overlooking the obvious!