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Completing The Square

Question 1 • AZ-Common Core Algebra II A

Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply.

Answer
A
x2 – 16x – 64
B
4x2 +12x + 9
C
x2 + 20x + 100
D
x2 + 4x + 16

Explanation

A perfect-square trinomial has the form a² + 2ab + b², so its first and last terms are squares and its middle term matches twice their roots’ product. For B, 4x² + 12x + 9 = (2x + 3)²; for C, x² + 20x + 100 = (x + 10)². A would need a constant term of +64 to be (x − 8)², and D does not have the middle term needed for a square.

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