Question

Identify the trinomial that is not a perfect square.

64x^2 + 48x + 9
100x^2 + 60x + 9
25x^2 + 70x + 49
121x^2 + 100x + 25

Answer 1

The trinomial that is not a perfect square is:

`100x^2 + 60x + 9`

To see why, we can try to factor each trinomial. For example:

`64x^2 + 48x + 9 = (8x + 3)^2`

`25x^2 + 70x + 49 = (5x + 7)^2`

`121x^2 + 100x + 25 = (11x + 5)^2`

Notice that each of these trinomials can be factored into the square of a binomial. However, for the trinomial

`100x^2 + 60x + 9`

we cannot find two binomials that will multiply to give this trinomial. Therefore, it is not a perfect square trinomial.