Answer
$$10x^7-3x^6- x^5+ 44x^4 +x^3 - x^2+16x -2 $$
Work Step by Step
We multiply each term of the first polynomial by each term of the second polynomial. Then we add the products, as follows
$$ (8x - x^3+ 2x^4 - 1)(x^2 +2 + 5x^3)\\ =8x (x^2 +2 + 5x^3) - x^3(x^2 +2 + 5x^3)+ 2x^4 (x^2 +2 + 5x^3) - 1(x^2 +2 + 5x^3) \\ =8x^3 +16x + 40x^4 - x^5 -2x^3 -5x^6+ 2x^6 +4x^4 + 10x^7 - x^2 -2 - 5x^3\\ =10x^7-3x^6- x^5+ 44x^4 +x^3 - x^2+16x -2 .$$
