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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinev2+8v+____v^2 + 8v + \_\_\_\_

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Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinev2+8v+____v^2 + 8v + \_\_\_\_
  1. Identify coefficients: Identify the coefficients of the polynomial v2+8v+?v^2 + 8v + ? by comparing it to the standard quadratic form ax2+bx+cax^2 + bx + c.
    a=1a = 1
    b=8b = 8
    c=?c = ?
  2. Calculate value: To complete the square, we need to add (b2)2(\frac{b}{2})^2 to the polynomial v2+8vv^2 + 8v.\newlineCalculate (82)2(\frac{8}{2})^2.\newline(82)2=(4)2=16(\frac{8}{2})^2 = (4)^2 = 16
  3. Add to make perfect-square: Add the calculated value to the polynomial to make it a perfect-square quadratic. v2+8v+16v^2 + 8v + 16 is now a perfect-square quadratic.

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