Answer:
When A = 48, the polynomial \(9x^2+Ax+64\) a perfect square trinomial.
Step-by-step explanation:
Given : the polynomial \(9x^2+Ax+64\)
We have to find the value of A that makes the polynomial a perfect square trinomial.
For a trinomial to be a perfect square trinomial when it can be written in form of a perfect square as \((a+b)^2=a^2+b^2+2ab\)
Consider the given polynomial \(9x^2+Ax+64\)
Comparing the given polynomial with the right side of the above identity,
\(9x^2+Ax+64\) can be written as \((3x)^2+Ax+(8)^2\)
We have,
a = 3x , b = 8
also , 2ab = Ax
2(3x)(8) = Ax
⇒ 48 = A
Thus, When A = 48, the polynomial \(9x^2+Ax+64\) a perfect square trinomial.
