# Can someone please explain how to determine whether the trinomial is a perfect square?

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electreto05 | College Teacher | (Level 1) Assistant Educator

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First, the maximum power of the variable must be 2. The first analysis is done for the coefficient of the term in x^2 and the independent term; the square root of these numbers must be accurate. Then, the product of the square roots above is performed, and the result is multiplied by 2; the result of this calculation must be equal to the coefficient of the term in x.

For the example given we have:

The coefficient of the term in x^2 is 9  →  √9 = 3

The independent term is 4  →  √4 = 2

So, these numbers have exact square roots. Multiplying these square roots by 2, we have:

2(3)(2) = 12, that is, the coefficient of the term in x.

If the trinomial, meet these conditions, then it is a perfect square trinomial.

steveschoen | College Teacher | (Level 1) Associate Educator

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Well, you could factor it like normal.  If you get the same parenthesis for an answer, then it is a perfect square.

For a shorter method, following the formula ax*2 + bx + c, consider:

is b^2 - 4ac = 0

If yes, then it is a perfect square.  If not, then no.

For instance, here, we have a = 9, b = -12, and c = 4.  So, plugging in the numbers:

(-12)^2 - 4*9*4 = 0

144 - 144 = 0

0 = 0

So, it would be a perfect square.