Final answer:
Numerical evidence from expanding (3x-5)(x-2) yields 3x^2 -11x + 10, which does not match the original quadratic expression 3x^2 - 11x - 20. The discrepancy lies in the constant term, proving that these factors are incorrect.
Step-by-step explanation:
The factors given for the quadratic expression 3x^2 - 11x - 20 as (3x-5)(x-2) do not work. To verify this, we can expand the factors to see if they result in the original expression. After expanding (3x-5)(x-2), we get:
3x * x = 3x^2
3x * -2 = -6x
-5 * x = -5x
-5 * -2 = 10
Combining these terms gives us: 3x^2 - 6x - 5x + 10 = 3x^2 - 11x + 10, which is not equal to the original expression 3x^2 - 11x - 20. The constant term here is +10, not -20.
Thus, the numerical evidence shows that when multiplying the factors (3x-5) and (x-2), the resulting expression is different from the given quadratic expression, which means that these factors do not correctly factorize the given quadratic.