Question
Which is a perfect square trinomial?(1 point)
Responses
x2−14x+49x squared minus 14 x plus 49
36x2−4x+3
Responses
x2−14x+49x squared minus 14 x plus 49
36x2−4x+3
Answers
GPT-4o mini
A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. The general form of a perfect square trinomial is \( (a \pm b)^2 = a^2 \pm 2ab + b^2 \).
Let's analyze the first expression:
1. \( x^2 - 14x + 49 \)
- We can rewrite this as \( (x - 7)^2 \), since \( (x - 7)(x - 7) = x^2 - 14x + 49 \).
Now for the second expression:
2. \( 36x^2 - 4x + 3 \)
- We can check if it can be factored into a perfect square. However, \( 36x^2 \), \( -4x \), and \( 3 \) do not appear to fit the form of \( (a \pm b)^2 \) since \( -4x \) does not correspond to \( 2ab \) for any integers \( a \) and \( b \).
Thus, the perfect square trinomial from the options given is:
**\( x^2 - 14x + 49 \)**.
Let's analyze the first expression:
1. \( x^2 - 14x + 49 \)
- We can rewrite this as \( (x - 7)^2 \), since \( (x - 7)(x - 7) = x^2 - 14x + 49 \).
Now for the second expression:
2. \( 36x^2 - 4x + 3 \)
- We can check if it can be factored into a perfect square. However, \( 36x^2 \), \( -4x \), and \( 3 \) do not appear to fit the form of \( (a \pm b)^2 \) since \( -4x \) does not correspond to \( 2ab \) for any integers \( a \) and \( b \).
Thus, the perfect square trinomial from the options given is:
**\( x^2 - 14x + 49 \)**.