Learn To Factor Quadratic Equations: Step-By-Step Guide With Examples

x^2 – 11x + 24

(x – 3)(x – 8)

To factor x^2 – 11x + 24, we need to find two numbers whose sum is -11 and whose product is (1)(24) = 24. These numbers are -3 and -8 (since -3 + (-8) = -11 and (-3)(-8) = 24).

Now we can rewrite x^2 – 11x + 24 as

x^2 – 3x – 8x + 24

Next, we group the terms, taking the common factors out of each group:

(x^2 – 3x) – (8x – 24)

Now we can factor each group separately:

x(x – 3) – 8(x – 3)

Notice that we have a common factor of (x – 3), which we can factor out:

(x – 3)(x – 8)

Therefore, x^2 – 11x + 24 factors as (x – 3)(x – 8).

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