Questions: Question 10, 1.3.45 HW Score: 53.33%, 8 of 15 points Points: 0 of 1 Factor the polynomial completely. Factor out the greatest common factor as necessary. c^2-14 cp+49 p^2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. c^2-14 cp+49 p^2= (Factor completely.) B. The polynomial cannot be factored.

Solution Steps

The given polynomial is: \[ c^{2} - 14 c p + 49 p^{2} \]

A perfect square trinomial has the form: \[ a^{2} - 2ab + b^{2} = (a - b)^{2} \] Compare the given polynomial with this form:

• \( a^{2} = c^{2} \) → \( a = c \)
• \( b^{2} = 49 p^{2} \) → \( b = 7p \)
• \( 2ab = 14 c p \) → \( 2 \cdot c \cdot 7p = 14 c p \)

Since the polynomial matches the form of a perfect square trinomial, it can be factored as: \[ c^{2} - 14 c p + 49 p^{2} = (c - 7p)^{2} \]

The factored form of the polynomial is: \[ c^{2} - 14 c p + 49 p^{2} = (c - 7p)^{2} \]

Final Answer