Question

Which polynomial is a perfect square trinomial?

A. 25x2 − 20x − 16
B. 9a2 − 30a − 25
C. 25b2 − 15b + 9
D. 16x2 − 24x + 9

Answer 1

find their factors

Answer 2

a perfect square trinomial is one which can be factored as \[(a+b)(a+b) = a*a+a*b+b*a+b*b=a^2+2ab+b^2\]
If you think about this for a moment, you should realize that this rules out any possibility answers where the constant term (the one at the end, not involving a variable) is negative. Only if you are willing to allow imaginary numbers in your factors will a perfect square trinomial have a negative constant term.

Answer 3

then, take the square root of the squared term and the constant term. if multiplying those two numbers together and then by 2 gives you the remaining term, you have a perfect square trinomial.

for example:

\[4x^2+2x+16\]square root of 4 is 2, square root of 16 is 4, but 2*4*2= 16, not 2, so this is not a perfect square trinomial.

\[x^2+4x+4\]square root of 1 is 1, square root of 4 is 2, 1*2*2=4 so this is a perfect square trinomial.