Final answer:
To factorize the given quadratic expression 2x² - 7x + 6, the correct answer is (2x - 3)(x - 2).
Step-by-step explanation:
To factorize the given quadratic expression 2x² - 7x + 6, we need to find two binomials whose product is equal to the given expression. We can solve this by using the AC method or by factoring trinomials.
By factoring, we find that the correct option is (2x - 3)(x - 2) which is option A.
The two numbers that satisfy these conditions are -3 and -4. So, the expression can be written as:
2x² - 3x - 4x + 6
Now, we can group the terms and factor by grouping:
(2x² - 3x) + (-4x + 6)
= x(2x - 3) -2(2x - 3)
= (x - 2)(2x - 3),
Therefore, the factorized form of the given expression is (2x - 3)(x - 2), which is option A).