Question: Factor completely. c^2 - 4c + 22 Select the correct choice below and, if necessary, fill in the…

Factor completely.

c^2 - 4c + 22

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. c^2 - 4c + 22 = (Factor completely.)

B. The polynomial is prime.

Solution

Step 1: Identify the quadratic expression. \[ c^2 - 4c + 22 \] Step 2: Compute the discriminant to determine if the polynomial can be factored. \[ D = b^2 - 4ac \] Step 3: Substitute the coefficients into the discriminant. \[ D = (-4)^2 - 4(1)(22) = 16 - 88 = -72 \] Step 4: Analyze the discriminant. Since \( D = -72 \) is less than 0, the polynomial does not have real roots and cannot be factored over the real numbers. Answer: B. The polynomial is prime.