Final answer:
To factor completely the expression -3x^2 + 17x - 20, you need to find two binomials that when multiplied together would give you the original expression. The factored form of the expression is (-3x + 5)(x - 4).
Step-by-step explanation:
To factor completely the expression -3x2 + 17x - 20, we need to find two binomials that when multiplied together would give us the original expression. First, we look for factors of the constant term (-20) that when added or subtracted would give us the coefficient of the middle term (17).
The factors of -20 are: -1, 1, -2, 2, -4, 4, -5, 5, -10, and 10. Testing out these pairs, we find that -4 and 5 add up to 1, which is the coefficient of the middle term. Therefore, the factored form of the expression is (-3x + 5)(x - 4).