Answer:
To factor -3x^2 + 17x - 20 completely, we need to find two binomials that when multiplied together give us the original quadratic expression.
First, we can multiply the leading coefficient (-3) by the constant term (-20) to get -60. Then, we need to find two numbers that multiply to -60 and add up to the coefficient of the x-term (17). After some trial and error, we find that the two numbers are 12 and -5.
Now, we can rewrite the quadratic expression as:
-3x^2 + 17x - 20 = -3x^2 + 12x - 5x - 20
Next, we group the first two terms and the last two terms:
(-3x^2 + 12x) + (-5x - 20)
We can factor out 3x from the first group and -5 from the second group:
3x(x - 4) - 5(x + 4)
Now we can factor out a negative one from the second grouping:
3x(x - 4) - 5( -1)(x + 4)
And simplify:
3x(x - 4) + 5(x + 4)
Therefore, the quadratic expression -3x^2 + 17x - 20 can be factored completely as (3x - 5)(x - 4).