Factoring Quadratic Expressions: Explained with an Example (x^2 + 5x + 6)

x^2 + 5x + 6

To solve the expression x^2 + 5x + 6, you can use factoring or the quadratic formula

To solve the expression x^2 + 5x + 6, you can use factoring or the quadratic formula. Let’s try factoring first.

We are looking for two numbers that multiply to give 6, and add up to give 5. The numbers that meet this criteria are 2 and 3. Therefore, we can factor the expression as follows:

(x + 2)(x + 3)

Now, we have two binomial terms, (x + 2) and (x + 3). To further simplify this expression, we can distribute the terms using the distributive property.

(x + 2)(x + 3) = x(x) + x(3) + 2(x) + 2(3)
= x^2 + 3x + 2x + 6
= x^2 + 5x + 6

So, the expression x^2 + 5x + 6 is equivalent to (x + 2)(x + 3).

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