What is the other factor of the polynomial x^2 + 5x + 36 if (x – 9) is one of its factors?

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To determine the other factor of the polynomial x2 + 5x + 36, given that (x – 9) is a factor, we can follow these steps:

  1. First, understand what factors are: Factors of a polynomial are expressions that can be multiplied together to obtain the original polynomial.
  2. Use polynomial long division: To find the other factor, we can divide the polynomial x2 + 5x + 36 by the given factor (x – 9).

Step 1: Perform the division:

     x + 14         _______________________x - 9 | x2 + 5x + 36         - (x2 - 9x)         _______________________                 14x + 36            - (14x - 126)         _______________________                             162

Step 2: Analyze the result: After performing the division, if the calculation was done correctly, and (x – 9) was indeed a factor, the remainder should be 0. In this case, the result we obtain from the division is x + 14.

Final Result: Thus, the complete factorization of the polynomial x2 + 5x + 36 is:

(x - 9)(x + 14)

In conclusion, if (x – 9) is a factor, the other factor is (x + 14).

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