Which model shows the correct factorization of x2 – x – 2?
Answer: The two factors of x2 - x - 2 are (x + 1) and (x - 2).
We will use the splitting of middle term method to factorise the given expression.
Given: x2 - x - 2
Firstly we need to find out two numbers whose product is equal to the constant term (3rd term) and whose sum will produce the coefficient of x i.e, 2nd term.
These numbers are 1 and - 2 respectively.
Product: 1 × (-2) = -2 (constant term)
Sum: 1 + (-2) = -1 (coefficient of x)
Now we can factor the above expression
= x2 + (1x - 2x) - 2
= x2 -2x + x - 2
= x (x - 2) + 1 (x - 2)
= (x + 1)(x - 2)