Answer:
(x - 2)(x + 1)
Explanation:
To factor the quadratic expression x^2 - x - 2, you need to find two binomials whose product equals the given expression. Here's how you can factor it:
Look for two numbers, let's call them "a" and "b," such that their product is equal to the product of the leading coefficient (1, the coefficient of x^2) and the constant term (-2). In this case, the product of a and b should be -2.
You also need to find two numbers "a" and "b" whose sum is equal to the coefficient of the linear term, which is -1 in this case.
The numbers that fit these criteria are a = -2 and b = 1 because (-2) * 1 = -2 and (-2) + 1 = -1.
Now that you have these numbers, you can use them to factor the expression. You split the middle term (-x) into two terms using a and b. This gives you:
x^2 - 2x + x - 2
Now, you can group the terms:
(x^2 - 2x) + (x - 2)
Factor out the greatest common factor from each group:
x(x - 2) + 1(x - 2)
You'll notice that both terms have a common factor of (x - 2). Factor that out:
(x - 2)(x + 1)
So, the factored form of x^2 - x - 2 is (x - 2)(x + 1).