Which are perfect square trinomials? Select two options.
x2 − 9
x2 −100
x2 − 4x + 4
x2 + 10x + 25
x2 + 15x + 36
it is clear that the first two fail, since they are binomials.
You know that (a+b)^2 = a^2 + 2ab + b^2
so first, check that the first and last terms are perfect squares.
the last three all pass that test.
now just check the middle term. 15 is odd, so it cannot be 2ab.
So, C,E are the answers
Which are perfect square trinomials? Select two options.
x2 − 9
x2 −100
x2 − 4x + 4
x2 + 10x + 25
x2 + 15x + 36
Perfect square trinomials are trinomials that can be factored into the square of a binomial. From the options provided, the two perfect square trinomials are:
1) x2 + 10x + 25
2) x2 + 15x + 36
These trinomials can be factored as:
1) (x + 5)(x + 5) = (x + 5)^2
2) (x + 6)(x + 6) = (x + 6)^2
To determine if a trinomial is a perfect square trinomial, we need to check if it can be factored into two identical binomials.
Let's go through each option:
1. x^2 - 9: This is not a perfect square trinomial because it can be factored as (x + 3)(x - 3), which gives two different binomials.
2. x^2 - 100: This is a perfect square trinomial because it can be factored as (x + 10)(x - 10), which gives two identical binomials.
3. x^2 - 4x + 4: This is a perfect square trinomial because it can be factored as (x - 2)(x - 2), which gives two identical binomials.
4. x^2 + 10x + 25: This is a perfect square trinomial because it can be factored as (x + 5)(x + 5), which gives two identical binomials.
5. x^2 + 15x + 36: This is a perfect square trinomial because it can be factored as (x + 6)(x + 6), which gives two identical binomials.
Therefore, the two options that represent perfect square trinomials are:
- x^2 - 4x + 4
- x^2 + 10x + 25