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.

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.
Transcript text: 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. \[ c^{2}-14 c p+49 p^{2} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $c^{2}-14 c p+49 p^{2}=\square$ (Factor completely.) B. The polynomial cannot be factored.
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Solution

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Solution Steps

Step 1: Identify the polynomial

The given polynomial is: c2−14cp+49p2 c^{2} - 14 c p + 49 p^{2}

Step 2: Check if it is a perfect square trinomial

A perfect square trinomial has the form: a2−2ab+b2=(a−b)2 a^{2} - 2ab + b^{2} = (a - b)^{2} Compare the given polynomial with this form:

  • a2=c2 a^{2} = c^{2} → a=c a = c
  • b2=49p2 b^{2} = 49 p^{2} → b=7p b = 7p
  • 2ab=14cp 2ab = 14 c p → 2⋅c⋅7p=14cp 2 \cdot c \cdot 7p = 14 c p

Since the polynomial matches the form of a perfect square trinomial, it can be factored as: c2−14cp+49p2=(c−7p)2 c^{2} - 14 c p + 49 p^{2} = (c - 7p)^{2}

Step 3: Write the factored form

The factored form of the polynomial is: c2−14cp+49p2=(c−7p)2 c^{2} - 14 c p + 49 p^{2} = (c - 7p)^{2}

Final Answer

(c−7p)2\boxed{(c - 7p)^{2}}

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