Question

What value in place of the question mark makes the polynomial below a perfect square trinomial? 9x2+?x+64

Answer 1

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.

Answer 2

9x² + bx + 64
\/(9x²) = 3x
\/84 = 8
2*3x*8 = 48x
b = 48