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 FOIL (First, Outer, Inner, Last). Here’s how it works:
Multiply the first terms of each binomial: x * x = x^2
Multiply the outer terms of each binomial: x * 3 = 3x
Multiply the inner terms of each binomial: 2 * x = 2x
Multiply the last terms of each binomial: 2 * 3 = 6
Add up the results of the previous steps: x^2 + 3x + 2x + 6
Simplify by combining like terms: x^2 + 5x + 6
So we have the expression x^2 + 5x + 6 = (x+2)(x+3). This is an example of factoring a quadratic trinomial, which can be useful for solving equations and graphing quadratic functions.
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