Factorize: x² - 5x + 6

A quadratic expression is a polynomial of degree 2. We can use middle term factorisation to solve this problem.

Answer: The Factors of x² - 5x + 6 are (x-3) (x-2)

Let us proceed by using middle term factorization

Explanation:

Step 1: Multiply the coefficient of the first term by the constant term i.e (6 x 1) = 6

Step 2: Find the two factors of 6  such that whose sum equals to the coefficient of the middle term, i.e -5.

Thus, the factors are -3 and -2 as,

-3 × (-2) = 6 (Product)

-3 + (-2) = -5 (Sum)

The polynomial  after splitting the middle term by using the two factors, -3 and -2 can be written as

x² - 3x - 2x + 6 = 0    

⇒ x(x-3) -2(x-3) = 0

⇒ (x-3)(x-2) = 0   

Thus, the Factors of x² - 5x + 6 are (x-3) (x-2).