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,
[tex]=x^2+5x-36\\\\=x^2+9x-4x-36\\\\=x(x+9)-4(x+9)\\\\=(x+9)(x-4)[/tex]
The given polynomial is
[tex]=(x+9)[/tex]
Let the other binomial is z, so
[tex]\Rightarrow (x+9)\times z=x^2+5x-36[/tex]
[tex]\Rightarrow z=\dfrac{x^2+5x-36}{x+9}[/tex]
[tex]\Rightarrow z=\dfrac{(x+9)(x-4)}{x+9}[/tex]
[tex]\Rightarrow z=(x-4)[/tex]
Therefore, the other binomial is [tex](x-4)[/tex]
