Question

What is the product of -2x^2 + x - 5 and x^3 - 3x - 4 ? Show your work.

Answer 1

For this case we must find the product of the following expressions:$(-2x ^ 2 + x-5) (x ^ 3-3x-4) =$

We must apply distributive property, that is, multiply each term:

We must bear in mind that:

$+ * - = -\\- * - = +$

$-2x ^ {2 + 3} + 6x^{2 + 1} + 8x ^ 2 + x^{3 + 1} -3x^{1 + 1} -4x-5x ^ 3 + 15x + 20 =\\-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20$

If we multiply$(x ^ 3-3x-4) (- 2x ^ 2 + x-5)$ we would obtain the same result according to the commutative property of the multiplication:

$a * b = b * a$

Answer:

$-2x ^ 5 + 6x ^ 3 + 8x ^ 2 + x ^ 4-3x ^ 2-4x-5x ^ 3 + 15x + 20$