Check Your Progress: Factor each \( t \) 1. \( x^{2}-9 x+14 \)

To factor the expression \( x^{2}-9x+14 \), look for two numbers that multiply to \( 14 \) (the constant term) and add up to \( -9 \) (the coefficient of \( x \)). The numbers \( -7 \) and \( -2 \) fit this requirement. Therefore, you can factor the quadratic as \( (x-7)(x-2) \). To check your work, you can expand \( (x-7)(x-2) \) to see if it equals the original expression: \( (x-7)(x-2) = x^2 - 2x - 7x + 14 = x^2 - 9x + 14 \). Ta-da! You've successfully factored the quadratic!