Final answer:
To factorize the expression 6x² + 5x - 6, we can split the middle term as 6x² + 6x - x - 6 and then factor by grouping as (6x - 1)(x + 6).
Step-by-step explanation:
The given expression is 6x² + 5x - 6. To factorize it, we need to find two numbers that multiply to give the product of the coefficient of x² (6) and the constant term (-6) and add up to the coefficient of x (5). In this case, the numbers are 6 and -1.
So, we can split the middle term as 6x² + 6x - x - 6.
Then, we can factor by grouping as (6x² + 6x) - (x + 6) = 6x(x + 1) - 1(x + 6) = (6x - 1)(x + 6).