Answer-
The binomial you can multiply by (x+9) is (x-4) to get the product x²+5x-36
Solution-
The product is given by,
\(=x^2+5x-36\\\\=x^2+9x-4x-36\\\\=x(x+9)-4(x+9)\\\\=(x+9)(x-4)\)
The given polynomial is
\(=(x+9)\)
Let the other binomial is z, so
\(\Rightarrow (x+9)\times z=x^2+5x-36\)
\(\Rightarrow z=\dfrac{x^2+5x-36}{x+9}\)
\(\Rightarrow z=\dfrac{(x+9)(x-4)}{x+9}\)
\(\Rightarrow z=(x-4)\)
Therefore, the other binomial is \((x-4)\)
