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.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the polynomial

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

Step 2: Check if it is a perfect square trinomial

A perfect square trinomial has the form: \[ a^{2} - 2ab + b^{2} = (a - b)^{2} \] 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: \[ c^{2} - 14 c p + 49 p^{2} = (c - 7p)^{2} \]

Step 3: Write the factored form

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

Final Answer

\(\boxed{(c - 7p)^{2}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
28) A tear of the tendons that hook the muscles of the forearm to the elbow is: - Ankylosis - Gout - Subluxation - Tennis elbow 29) What does the word part Bucco- mean?
failedAnswered
Bank of América Balance Sheet (in billions) Assets Liabilities Reserves 50 Deposits 500 Bonds 190 Loans Net Worth 40 Using the bank balance sheet above and assuming a reserve requirement of 10%, select all statement below that are true. If this bank makes a 2 billion loan to a large corporation, its "Net Worth" will go down by 2 billion. If this bank makes a 2 billion loan to a large corporation its "Reserves" will decrease by 2 billion In the event of a Bank Run and absent Fed intervention, this bank will not have sufficient reserves to meet depositors demands. If the Fed engages in an open market purchase of 25 billion, this bank will be able to increase "Loans" by 22.5 billion. If the Fed engages in an open market sale of 50 billion, the net worth of this bank will not change.
failedAnswered
Multiple Choice Question When meiosis occurs without recombination, which of the following has occurred? Aneuploidy Achiasmate segregation Non-independent assortment Need help? Review these concept resources.
failedAnswered
What is the formula for amme In the VSEPR model, the geometry of the regions defined by the electron pairs in the valence shell of an atom is called the electron-pair geometry. A. The Lewis diagram for SbF3 is: The electron-pair geometry around the Sb atom in SbF3 is There are unshared pair(s) around the central atom, so the geometry of the SbF3 molecule is .
failedAnswered
Describe the local behavior of the function shown in the graph above. As x approaches -4 from the left, f(x) approaches Select an answer As x approaches -4 from the right, f(x) approaches Select an answer Describe the long run behavior of the function shown in the graph above. As x approaches infinity, f(x) approaches Select an answer As x approaches negative infinity, f(x) approaches Select an answer