Perfect Square Trinomial Puzzle

What is the trinomial that represents a perfect square?

Choose the correct trinomial:

a. x^2 + 4x + 4

b. 2x^2 - 5x + 2

c. 3x^2 + 12x + 9

d. -6x^2 + 11x - 5

The correct trinomial that represents a perfect square is:

c. 3x^2 + 12x + 9

A perfect square trinomial is a trinomial that can be factored into a perfect square of a binomial. In this case, the trinomial "3x^2 + 12x + 9" can be factored into (3x + 3)^2, which is a perfect square.

The process of factoring a perfect square trinomial involves taking the square root of the first and last term, and then eliminating the middle term by making it the product of the square root of the first and last term. In this case, the square root of 3x^2 is 3x, and the square root of 9 is 3. Multiplying these, we get 3x * 3 = 9x. Therefore, the factored form is (3x + 3)^2.

It is important to recognize the patterns of perfect square trinomials in order to quickly identify and factor them correctly.