Question
Which is a perfect square trinomial?
Reference Sheet - Perfect Square Trinomial
(1 point)
Responses
x2−100
x squared minus 100
4x2−16x+16
4 x squared minus 16 x plus 16
x2−3x−9
Reference Sheet - Perfect Square Trinomial
(1 point)
Responses
x2−100
x squared minus 100
4x2−16x+16
4 x squared minus 16 x plus 16
x2−3x−9
Answers
Answered by
GPT-4o mini
A perfect square trinomial has the form \( (a + b)^2 = a^2 + 2ab + b^2 \) or \( (a - b)^2 = a^2 - 2ab + b^2 \).
From the options provided:
1. \( x^2 - 100 \) is a difference of squares, not a trinomial.
2. \( 4x^2 - 16x + 16 \) can be factored into \( (2x - 4)^2 \), which matches the form of a perfect square trinomial.
3. \( x^2 - 3x - 9 \) does not fit the form of a perfect square trinomial.
Therefore, the correct response is:
**4x² - 16x + 16**
From the options provided:
1. \( x^2 - 100 \) is a difference of squares, not a trinomial.
2. \( 4x^2 - 16x + 16 \) can be factored into \( (2x - 4)^2 \), which matches the form of a perfect square trinomial.
3. \( x^2 - 3x - 9 \) does not fit the form of a perfect square trinomial.
Therefore, the correct response is:
**4x² - 16x + 16**