Find the product

7x(-2x^2+x-4)

7X(-2X^2+X-4).

Multiply each term within the parenthesis by 7X:

-14X^3 + 7X^2 - -28X.

To find the product of 7x and (-2x^2 + x - 4), we need to distribute 7x across each term inside the parentheses.

First, distribute 7x across -2x^2:
7x * -2x^2 = -14x^3

Next, distribute 7x across x:
7x * x = 7x^2

Lastly, distribute 7x across -4:
7x * -4 = -28x

Putting it all together, the product of 7x and (-2x^2 + x - 4) is:
-14x^3 + 7x^2 - 28x