Final Answer;
1. Yes, m² - 6m + 9 is a perfect square trinomial and factors as (m - 3)² .
2. No, 99n² + 30n + 252w² is not a perfect square trinomial.
3. No, 4w + 94d² - 4d + 1 is not a perfect square trinomial.
Step-by-step explanation:
The first trinomial, m² - 6m + 9, is a perfect square trinomial because it can be factored as (m - 3)² This can be confirmed by expanding (m - 3)² to get m² - 6m + 9.
For the second and third trinomials, 99n² + 30n + 252w² and 4w + 94d² - 4d + 1, the discriminant is calculated to determine if they are perfect square trinomials. If the discriminant is greater than zero, the trinomial is not a perfect square. In both cases, the discriminant is indeed greater than zero, confirming that these trinomials do not factor into perfect squares.
Let's analyze each trinomial to determine if it is a perfect square trinomial:
1. m² - 6m + 9 - This trinomial is a perfect square trinomial since it can be factored as (m - 3)² .
2. 99n² + 30n + 252w² - This trinomial is not a perfect square trinomial. To determine this, we can calculate the discriminant (b² - 4ac) of the quadratic equation 99n² + 30n + 252w² = 0, where (a = 99),(b = 30), and (c = 252w² ). The discriminant is (30² - 4(99)(252w² ), which is greater than zero, indicating that the trinomial does not factor into a perfect square.
3. 4w + 94d² - 4d + 1 - This trinomial is not a perfect square trinomial. Similar to the second trinomial, we can calculate the discriminant of the quadratic equation 94d² - 4d + 1 = 0, and the result is greater than zero, indicating that it is not a perfect square trinomial.
In summary:
1. m² - 6m + 9 is a perfect square trinomial and factors as (m - 3)² .
2. 99n² + 30n + 252w² is not a perfect square trinomial.
3. 4w + 94d² - 4d + 1 is not a perfect square trinomial.