Multiply each term of $ \left( \color{blue}{x^2+3}\right) $ by each term in $ \left( 2x-8\right) $.

$$ \left( \color{blue}{x^2+3}\right) \cdot \left( 2x-8\right) = 2x^3-8x^2+6x-24 $$

Multiply each term of $ \left( \color{blue}{2x^3-8x^2+6x-24}\right) $ by each term in $ \left( x-5\right) $.

$$ \left( \color{blue}{2x^3-8x^2+6x-24}\right) \cdot \left( x-5\right) = 2x^4-10x^3-8x^3+40x^2+6x^2-30x-24x+120 $$

Combine like terms:

$$ 2x^4 \color{blue}{-10x^3} \color{blue}{-8x^3} + \color{red}{40x^2} + \color{red}{6x^2} \color{green}{-30x} \color{green}{-24x} +120 = \\ = 2x^4 \color{blue}{-18x^3} + \color{red}{46x^2} \color{green}{-54x} +120 $$

Multiply each term of $ \left( \color{blue}{2x^4-18x^3+46x^2-54x+120}\right) $ by each term in $ \left( x-2\right) $.

$$ \left( \color{blue}{2x^4-18x^3+46x^2-54x+120}\right) \cdot \left( x-2\right) = \\ = 2x^5-4x^4-18x^4+36x^3+46x^3-92x^2-54x^2+108x+120x-240 $$

Combine like terms:

$$ 2x^5 \color{blue}{-4x^4} \color{blue}{-18x^4} + \color{red}{36x^3} + \color{red}{46x^3} \color{green}{-92x^2} \color{green}{-54x^2} + \color{orange}{108x} + \color{orange}{120x} -240 = \\ = 2x^5 \color{blue}{-22x^4} + \color{red}{82x^3} \color{green}{-146x^2} + \color{orange}{228x} -240 $$