Question
Which of these is a perfect square trinomial?
Reference sheet
(2 points)
Responses
x2−100
x squared minus 100
4x2−16x +16
4x2−16x +16
x2−3x − 9
x2−3x − 9
49x + 16
Reference sheet
(2 points)
Responses
x2−100
x squared minus 100
4x2−16x +16
4x2−16x +16
x2−3x − 9
x2−3x − 9
49x + 16
Answers
GPT-4o mini
A perfect square trinomial is an expression that can be factored into the square of a binomial. The general form of a perfect square trinomial is \(a^2 + 2ab + b^2\) or \(a^2 - 2ab + b^2\).
From the options provided, let's analyze them:
1. **x² - 100**: This is a difference of squares, not a trinomial.
2. **4x² - 16x + 16**: This can be factored as \((2x - 4)²\), which shows it is a perfect square trinomial.
3. **x² - 3x - 9**: This cannot be factored into a perfect square trinomial.
4. **49x + 16**: This is a binomial, not a trinomial, and does not fit the perfect square trinomial pattern.
Thus, the response that is a perfect square trinomial is:
**4x² - 16x + 16**.
From the options provided, let's analyze them:
1. **x² - 100**: This is a difference of squares, not a trinomial.
2. **4x² - 16x + 16**: This can be factored as \((2x - 4)²\), which shows it is a perfect square trinomial.
3. **x² - 3x - 9**: This cannot be factored into a perfect square trinomial.
4. **49x + 16**: This is a binomial, not a trinomial, and does not fit the perfect square trinomial pattern.
Thus, the response that is a perfect square trinomial is:
**4x² - 16x + 16**.