Learn How To Factor Quadratic Expressions Using The Grouping Technique: X^2 – 5X + 6 = (X-2)(X-3)

x^2 – 5x + 6

(x – 2)(x – 3)

The expression x^2 – 5x + 6 can be factored as (x-2)(x-3).

To see why, you can use the factoring technique known as grouping. Here’s how it works:

Look at the coefficient of x^2, which is 1. This means that the factors must have the form (x + ?)(x + ?).
Look at the constant term, which is 6. This means that the factors must have a product of 6.
Look for two numbers whose product is 6 and whose sum is the coefficient of x, which is -5. These numbers are -2 and -3.
Rewrite the expression as x^2 – 2x – 3x + 6, grouping the first two terms and the last two terms: (x^2 – 2x) + (-3x + 6).
Factor out the greatest common factor from each group: x(x-2) – 3(x-2).
Combine the terms with a common factor: (x-2)(x-3).
So we have the expression x^2 – 5x + 6 = (x-2)(x-3).

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