Which model shows the correct factorization of x² - x - 2?

Solution:

Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic 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)

Hence, the two factors of x² - x - 2 are (x + 1) and (x - 2).

Which model shows the correct factorization of x² - x - 2?

Summary:

The two factors of x² - x - 2 are (x + 1) and (x - 2).