Simplifying the Expression x^2 – 5x + 6: Quadratic Formula and Factoring Methods Explained

x^2 – 5x + 6

To simplify the expression x^2 – 5x + 6, we can use the quadratic formula or factor it

To simplify the expression x^2 – 5x + 6, we can use the quadratic formula or factor it.

1. Factoring method:
The given expression x^2 – 5x + 6 can be written as (x – 2)(x – 3) by factoring.
To factor this quadratic expression, we need to find two numbers that add up to -5 and multiply to get 6. The numbers are -2 and -3 since (-2) + (-3) = -5 and (-2) * (-3) = 6.
So, x^2 – 5x + 6 can be factored as (x – 2)(x – 3).

2. Quadratic formula:
If you prefer to use the quadratic formula, which can be used for any quadratic expression, you can use the formula:
x = (-b ± √(b^2 – 4ac)) / (2a)
Here, a = 1, b = -5, and c = 6.

Inserting these values in the quadratic formula:
x = (-(-5) ± √((-5)^2 – 4*1*6)) / (2*1)
Simplifying,
x = (5 ± √(25 – 24)) / 2
x = (5 ± √1) / 2
x = (5 ± 1) / 2

This gives us two possible solutions:
x = (5 + 1) / 2 = 6 / 2 = 3
x = (5 – 1) / 2 = 4 / 2 = 2

So, the quadratic expression x^2 – 5x + 6 can be factored as (x – 2)(x – 3), and the solutions are x = 2 and x = 3.

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