x(3x^2 - 5x + 8)
When you distribute a constant, you multiply it. Here, it's to each value within the parentheses. So:
x(3x2 - 5x +8) = 3x2(x) - 5x(x) + 8(x)
When multiplying unknown variables (like 'x'), the product is that variable raised to the sum (addition) of their power.
For example: x3(x2) = x3+2 = x5 , or: y5(y4) = y5+4 = y9
Also, a variable with 'no exponent' actually has an exponent of 1. So, x = x1.
For example: x3(x) = x3+1 = x4
To finish your question,
3x2(x) - 5x(x) + 8(x) = 3x2+1 - 5x1+1 + 8x = 3x3 - 5x2 + 8x