It \( x+2 \) a factor of \( x^{2}+7 x-9 \).

To determine if \( x+2 \) is a factor of \( x^{2}+7x-9 \), we can use the factor theorem. According to the factor theorem, if \( x-a \) is a factor of \( f(x) \), then \( f(a) = 0 \). Given that \( x+2 \) is a factor, we substitute \( x = -2 \) into the polynomial \( x^{2}+7x-9 \) and check if the result is equal to 0. Substitute \( x = -2 \) into the polynomial: \[ (-2)^{2} + 7(-2) - 9 \] Now, let's calculate the result. Calculate the value by following steps: - step0: Calculate: \(\left(-2\right)^{2}+7\left(-2\right)-9\) - step1: Multiply the numbers: \(\left(-2\right)^{2}-14-9\) - step2: Evaluate the power: \(4-14-9\) - step3: Subtract the numbers: \(-19\) The result of substituting \( x = -2 \) into the polynomial \( x^{2}+7x-9 \) is -19, which is not equal to 0. Therefore, \( x+2 \) is not a factor of \( x^{2}+7x-9 \).