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Which of the following is a perfect square trinomial?

(A) 4x2 - 4x + 1

(B) 4x2 - 2x + 2

(C) 4x2 - 4x + 2

(D) 4x2 - 8x + 16

(E) 4x2 - 12x + 16

User Wogsland
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1 Answer

4 votes

Answer:

(A) 4x2 - 4x + 1

Explanation:

We can factor 4 out of each of these choices and see which ones can be factored as a perfect square

(A) 4x² - 4x + 1

= 4(x² - 1x + 1/4)

If x² - x + 1/4 is to be a perfect square, since the coefficient of x is negative it must be of the form (x - a)²
(x - a)² = x² - 2ax + a²

With a = 1/2, a² = 1/4

-2ax = -2 x 1/2 x = -1x = -x

So 4x2 - 4x + 1 is a perfect square and can be factored as
4(x - 1/2)²

User BruneauB
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