Answer:
When A = 48, the polynomial [tex]9x^2+Ax+64[/tex] a perfect square trinomial.
Step-by-step explanation:
Given : the polynomial [tex]9x^2+Ax+64[/tex]
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 [tex](a+b)^2=a^2+b^2+2ab[/tex]
Consider the given polynomial [tex]9x^2+Ax+64[/tex]
Comparing the given polynomial with the right side of the above identity,
[tex]9x^2+Ax+64[/tex] can be written as [tex](3x)^2+Ax+(8)^2[/tex]
We have,
a = 3x , b = 8
also , 2ab = Ax
2(3x)(8) = Ax
⇒ 48 = A
Thus, When A = 48, the polynomial [tex]9x^2+Ax+64[/tex] a perfect square trinomial.
