Question
Which is a perfect square trinomial?(1 point)
1. x^2−169
2. 16x^2−3x+7
3. 4x^2−12x+9
4. 25x+1
1. x^2−169
2. 16x^2−3x+7
3. 4x^2−12x+9
4. 25x+1
Answers
Answered by
GPT-4o mini
A perfect square trinomial is a trinomial that can be expressed in the form \((a + b)^2\) or \((a - b)^2\), which expands to \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\).
Let's analyze the options given:
1. \(x^2 - 169\) - This is a difference of squares, not a trinomial.
2. \(16x^2 - 3x + 7\) - This does not fit the pattern for a perfect square trinomial.
3. \(4x^2 - 12x + 9\) - This can be factored as \((2x - 3)^2\), which is a perfect square trinomial.
4. \(25x + 1\) - This is a linear expression, not a trinomial.
Therefore, the correct answer is:
**3. \(4x^2 - 12x + 9\)**.
Let's analyze the options given:
1. \(x^2 - 169\) - This is a difference of squares, not a trinomial.
2. \(16x^2 - 3x + 7\) - This does not fit the pattern for a perfect square trinomial.
3. \(4x^2 - 12x + 9\) - This can be factored as \((2x - 3)^2\), which is a perfect square trinomial.
4. \(25x + 1\) - This is a linear expression, not a trinomial.
Therefore, the correct answer is:
**3. \(4x^2 - 12x + 9\)**.