To find the product of -x^2 + 2x - 5 and 3x + 2, we can use the distributive property.
The product can be found by multiplying each term in the first expression by each term in the second expression.
- x^2 * 3x = -3x^3
- x^2 * 2 = -2x^2
- x^2 * 2 = -2x^2
2x * 3x = 6x^2
2x * 2 = 4x
2x * 2 = 4x
-5 * 3x = -15x
-5 * 2 = -10
Now we can add up the products:
-3x^3 - 2x^2 - 2x^2 + 6x^2 + 4x + 4x - 15x - 10
Combining like terms:
-3x^3 + 2x^2 + 8x - 10
Therefore, the product of -x^2 + 2x - 5 and 3x + 2 is:
-3x^3 + 2x^2 + 8x - 10.