Set the polynomial to zero and solve: \( x^{2} - 9x + 14 = 0 \)

To solve the polynomial \( x^{2} - 9x + 14 = 0 \), we can factor it. We're looking for two numbers that multiply to \( 14 \) (the constant term) and add up to \( -9 \) (the coefficient of \( x \)). These numbers are \( -7 \) and \( -2 \). So, we can factor the polynomial as follows: \[ (x - 7)(x - 2) = 0 \] Setting each factor equal to zero gives us the solutions: 1. \( x - 7 = 0 \) → \( x = 7 \) 2. \( x - 2 = 0 \) → \( x = 2 \) Thus, the solutions to the equation \( x^{2} - 9x + 14 = 0 \) are \( x = 7 \) and \( x = 2 \). Now, if you want to check your work, try plugging these values back into the original equation to see if they satisfy it—math is more fun when you double-check your answers!