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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinep2+2p+____p^2 + 2p + \_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinep2+2p+____p^2 + 2p + \_\_\_\_
  1. Identify values: Identify the values of aa, bb, and cc in the polynomial p2+2p+?p^2 + 2p + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1
    b=2b = 2
    c=?c = ?
  2. Determine completion: Determine the number that completes the square. To complete the square for the expression p2+2pp^2 + 2p, add (b/2)2(b/2)^2. Calculate (2/2)2(2/2)^2 to find the value that completes the square. (2/2)2=(1)2=1(2/2)^2 = (1)^2 = 1
  3. Find missing number: The missing number that makes the polynomial a perfect-square quadratic is 11. So, the complete expression is p2+2p+1p^2 + 2p + 1.

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