Final answer:
The quadratic expression 3x²-19x+20 can be factorized by finding two numbers that multiply to 60 (the product of the coefficient of x² and the constant term) and add up to -19, which are -15 and -4. This leads to the factorized form of the expression as (3x - 4)(x - 5).
Step-by-step explanation:
The student has asked to factorize the quadratic expression 3x²-19x+20. Factorization of a quadratic expression typically involves finding two binomials that when multiplied together, give back the original quadratic expression. To factorize the given expression, we are essentially looking for two numbers that multiply to give ac (where a is the coefficient of x² and c is the constant term) and add to give b (the coefficient of x).
In this case, a = 3 and c = 20, so ac = 60. We need two numbers that multiply to 60 and add up to -19 (the coefficient of x). These two numbers are -15 and -4.
Therefore, we can write the given expression as:
3x² - 15x - 4x + 20
Now, we group terms:
(3x² - 15x) - (4x - 20)
We can factor out a common factor from each group:
3x(x - 5) - 4(x - 5)
Since (x - 5) is common in both terms, we can factor it out:
(3x - 4)(x - 5)
So, the factorized form of the quadratic expression 3x²-19x+20 is (3x - 4)(x - 5).