Final answer:
Option D) (x - 3) is the factor of the quadratic expression 2x^2 - 22x + 48 because when x = 3 is substituted into the expression, the result is zero.
Step-by-step explanation:
To determine which of the options provided is a factor of the quadratic expression 2x2 - 22x + 48, we need to see if any of the options, when set equal to zero, would satisfy the given quadratic equation. This could be done by attempting to factor the expression or by using direct substitution.
First, let’s check option A) (x + 8). If we substitute x = -8 into the original expression to see if it equals zero we get: 2(-8)2 - 22(-8) + 48 = 128 + 176 + 48 = 352, which does not equal zero.
Now, let’s check option B) (x + 3). Substituting x = -3 into the quadratic expression we get: 2(-3)2 - 22(-3) + 48 = 18 + 66 + 48 = 132, which also does not equal zero.
The constant 24 (option C) cannot be a factor of the quadratic equation as it lacks the variable x.
Finally, option D) (x - 3). Using substitution, x = 3: 2(3)2 - 22(3) + 48 = 18 - 66 + 48 = 0. Since the expression equals zero when x = 3, option D) (x - 3) is indeed a factor of the quadratic expression.