x^2 + 13x + 36
(x + 4)(x + 9)
The expression x^2 + 13x + 36 can be factored as (x+9)(x+4).
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 * 4 = 4x
Multiply the inner terms of each binomial: 9 * x = 9x
Multiply the last terms of each binomial: 9 * 4 = 36
Add up the results of the previous steps: x^2 + 4x + 9x + 36
Simplify by combining like terms: x^2 + 13x + 36
So we have the expression x^2 + 13x + 36 = (x+9)(x+4). This is an example of factoring a quadratic trinomial, which can be useful for solving equations and graphing quadratic functions.
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