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Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic. $\newline$ $f^2 + 8f + \_\_\_\_\_$

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Complete the square

Full solution

Q. Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

\newline

f^2 + 8f + \_\_\_\_\_

Identify values: Identify the values of $a$ , $b$ , and $c$ in the polynomial $f^2 + 8f + ?$ by comparing it to the standard quadratic form $ax^2 + bx + c$ .
$a = 1$
$b = 8$
$c = ?$
Calculate square: To complete the square, we need to add $(\frac{b}{2})^2$ to the polynomial $f^2 + 8f$ . Calculate $(\frac{8}{2})^2$ . $\newline$ $(\frac{8}{2})^2 = (4)^2 = 16$
Complete the square: The number that completes the square and makes the polynomial a perfect-square quadratic is $16$ . So the polynomial becomes $f^2 + 8f + 16$ .

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