Question

Which of the following expressions are perfect square trinomials? (Select all that apply).

A) x² + 4x + 10
B) x² + 12x + 36
C) 4x² - 8x - 25
D) 9x² + 30x + 25

Answer 1

To determine which expressions are perfect square trinomials, we need to check if they can be factored into the square of a binomial. Only options B) and D) can be factored in this form.

Step-by-step explanation:

Perfect square trinomials are expressions that can be factored into the square of a binomial. To determine which expressions are perfect square trinomials, we need to check if they can be factored in the form (ax + b)². Let's analyze the given options:

1. A) x² + 4x + 10: This trinomial cannot be factored into the square of a binomial, so it is not a perfect square trinomial.
2. B) x² + 12x + 36: This trinomial can be factored into (x + 6)², so it is a perfect square trinomial.
3. C) 4x² - 8x - 25: This trinomial cannot be factored into the square of a binomial, so it is not a perfect square trinomial.
4. D) 9x² + 30x + 25: This trinomial can be factored into (3x + 5)², so it is a perfect square trinomial.

Therefore, the perfect square trinomials are B) x² + 12x + 36 and D) 9x² + 30x + 25.