Multiply each term of $ \left( \color{blue}{2x+3}\right) $ by each term in $ \left( x-5\right) $.

$$ \left( \color{blue}{2x+3}\right) \cdot \left( x-5\right) = 2x^2-10x+3x-15 $$

Combine like terms:

$$ 2x^2 \color{blue}{-10x} + \color{blue}{3x} -15 = 2x^2 \color{blue}{-7x} -15 $$

Multiply each term of $ \left( \color{blue}{2x^2-7x-15}\right) $ by each term in $ \left( x-2\right) $.

$$ \left( \color{blue}{2x^2-7x-15}\right) \cdot \left( x-2\right) = 2x^3-4x^2-7x^2+14x-15x+30 $$

Combine like terms:

$$ 2x^3 \color{blue}{-4x^2} \color{blue}{-7x^2} + \color{red}{14x} \color{red}{-15x} +30 = 2x^3 \color{blue}{-11x^2} \color{red}{-x} +30 $$

Multiply each term of $ \left( \color{blue}{2x^3-11x^2-x+30}\right) $ by each term in $ \left( x+1\right) $.

$$ \left( \color{blue}{2x^3-11x^2-x+30}\right) \cdot \left( x+1\right) = 2x^4+2x^3-11x^3-11x^2-x^2-x+30x+30 $$

Combine like terms:

$$ 2x^4+ \color{blue}{2x^3} \color{blue}{-11x^3} \color{red}{-11x^2} \color{red}{-x^2} \color{green}{-x} + \color{green}{30x} +30 = 2x^4 \color{blue}{-9x^3} \color{red}{-12x^2} + \color{green}{29x} +30 $$