We are given the following polynomial
[tex](x+3)(3x-1)(x-5)_{}[/tex]
Let us multiply and simplify the polynomial.
First, multiply any two parentheses and simplify
[tex](x+3)(3x-1)(x-5)_{}=(x\cdot3x+x\cdot-1+3\cdot3x+3\cdot-1)(x-5)_{}=(3x^2-x+9x-3)(x-5)=(3x^2+8x-3)(x-5)[/tex]
Now, multiply the remaining two parentheses
[tex](3x^2+8x-3)(x-5)=3x^2\cdot x+3x^2\cdot-5+8x\cdot x+8x\cdot-5-3\cdot x-3\cdot-5=3x^3-15x^2+8x^2-40x-3x+15=3x^3-7x^2-43x+15[/tex]
Therefore, the expanded polynomial is
[tex]3x^3-7x^2-43x+15[/tex]
