Factorizing the Quadratic Expression x^2 – 10x + 24 – A Step-by-Step Guide

x^2 – 10x + 24

To understand the given expression, let’s break it down step by step:

The given expression is x^2 – 10x + 24

To understand the given expression, let’s break it down step by step:

The given expression is x^2 – 10x + 24.

This expression represents a quadratic equation in standard form, ax^2 + bx + c, where in this case, a = 1, b = -10, and c = 24.

To factorize the given quadratic equation, we can use the product-sum method or the quadratic formula. Let’s use the product-sum method in this case.

We need to find two numbers whose product is equal to ac (a multiplied by c) and whose sum is equal to b.

In this case, ac = 1 * 24 = 24 and b = -10.

Now, we need to find two numbers that multiply to give 24 and add up to -10.

The numbers that meet these conditions are -4 and -6.

Therefore, we can rewrite the quadratic equation as follows:

x^2 – 4x – 6x + 24

Now, we group the terms and factor by grouping:

(x^2 – 4x) + (-6x + 24)

Now, we can factor out the greatest common factor from each group:

x(x – 4) – 6(x – 4)

Notice that x – 4 is common to both terms.

(x – 4)(x – 6)

Hence, the factorized form of the given expression x^2 – 10x + 24 is (x – 4)(x – 6).

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