\[
9 x^{2}-16=(n x+r)(n x-r)
\]
In the equation above, $r$ and $n$ are constants, Which of the following could be the value of $n$ ?
A) 2
B) 3
C) 4
D) 9
Answer
Final Answer: The value of \(n\) could be \(\boxed{3}\).
Step 1 ：The equation is in the form of a difference of squares, which can be factored as \((a+b)(a-b)\) where \(a\) and \(b\) are the square roots of the first and second terms respectively.
Step 2 ：In this case, \(a\) is the square root of \(9x^2\) which is \(3x\), and \(b\) is the square root of \(16\) which is \(4\).
Step 3 ：So, the factored form of the equation is \((3x+4)(3x-4)\).
Step 4 ：Comparing this with the given form \((nx+r)(nx-r)\), we can see that \(n\) is the coefficient of \(x\), which is \(3\).
Step 5 ：Final Answer: The value of \(n\) could be \(\boxed{3}\).
