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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinep2−4p+_____p^2 - 4p + \_\_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinep2−4p+_____p^2 - 4p + \_\_\_\_\_
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic expression p2−4p+?p^2 − 4p + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1
    b=−4b = -4
    bb00
  2. Determine perfect-square quadratic: Determine the number that needs to be added to p2−4pp^2 - 4p to make it a perfect-square quadratic. To complete the square, add (b/2)2(b/2)^2 to the expression.\newlinePerfect square quadratic: p2−4p+(b/2)2p^2 - 4p + (b/2)^2
  3. Calculate missing number: Calculate (b/2)2(b/2)^2 to find the missing number in p2−4p+____p^2 − 4p + \_\_\_\_.\newline(b/2)2=(−4/2)2(b/2)^2 = (-4/2)^2\newline=(−2)2= (-2)^2\newline=4= 4\newlineThe missing number is 44.

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