Question

which value is needed in the expression below to create a perfect square trinomial?
x²+8x+______
○ 4
○ 8
○ 16
○ 64

Explanation:

Step1: Recall the formula for a perfect square trinomial

A perfect square trinomial has the form \( (a + b)^2 = a^2 + 2ab + b^2 \). For the given expression \( x^2 + 8x + \_\_\_ \), we can identify \( a = x \) and \( 2ab = 8x \).

Step2: Solve for \( b \)

Substitute \( a = x \) into \( 2ab = 8x \): \( 2(x)b = 8x \). Divide both sides by \( 2x \) (assuming \( x
eq 0 \)): \( b = \frac{8x}{2x} = 4 \).

Step3: Find the constant term

The constant term of the perfect square trinomial is \( b^2 \). Since \( b = 4 \), then \( b^2 = 4^2 = 16 \).

Answer:

16 (corresponding to the option with value 16, i.e., the option "16")