Simplified Expression: Factoring x^2 + 13x + 36 into (x + 4)(x + 9)

x^2 + 13x + 36

To simplify the expression x^2 + 13x + 36, we need to see if it can be factored

To simplify the expression x^2 + 13x + 36, we need to see if it can be factored. To do this, we look for two numbers that multiply to give 36 and add up to 13.

The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

The pairs of numbers that add up to 13 are:
1 + 36 = 37
2 + 18 = 20
3 + 12 = 15
4 + 9 = 13 <== This pair adds up to 13 Since the pair 4 + 9 adds up to 13, we can rewrite the expression as follows: x^2 + 4x + 9x + 36 Now, we group the terms: (x^2 + 4x) + (9x + 36) We can factor out the greatest common factor from each group: x(x + 4) + 9(x + 4) Notice that we now have a common factor, (x + 4), in both terms. We can factor it out: (x + 4)(x + 9) Therefore, the simplified form of the expression x^2 + 13x + 36 is (x + 4)(x + 9).

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