Question

Determine which polynomial is a perfect square trinomial.

4x2 − 12x + 9
16x2 + 24x − 9
4a2 − 10a + 25
36b2 − 24b − 16

Answer 1

The answer is A.

Explanation:

To find perfect square trinomials you need to take the square root out of the first term in the polynomial and multiply that by the square root of the last term in the polynomial and then multiply those together by 2 and if it equals to the middle term then it is a perfect square trinomial. Answers C and D are wrong since when you multiply the square root of the first and last terms of the polynomial you get the middle term of the polynomial but, we need to multiply 2 as well which makes it not equal the middle term. Now, A and B both follow the perfect square trinomials but there is one clear difference that I didn't mention. Every perfect square trinomial follows the signs a^2 + 2ab + b^2 or it follows the signs a^2 - 2ab + b^2. Option B doesn't follow these signs but, Option A does making it the correct answer. Hope this helps you!

Answer 2

Trinomial Ax^2 + Bx + C is perfect square if:
A > 0
C > 0
B = ±2√A√C

36b^2 − 24b − 16
C < 0

4a^2 − 10a + 25
2√A√C = 2*2*5 = 20,
B = −10

16x^2 + 24x − 9
not perfect square,
C < 0

4x^2 − 12x + 9
perfect square:
A>0,
C>0,
2√A√C
= 2*2*3
= 12
= -B
= (2x − 3)^2
hope this helps