Question

If x -6 is one factor of x^2 - 10x +24, which is the other factor?

Answer 1

To get the other factor of the expression x² - 10x + 24, we can use long or synthetic division. We are given that the other factor is x - 6, so we can use that as our divisor. Our setup should look something like this:
x² - 10x + 24 ÷ x - 6
Here is the work using polynomial long division:
          x     -4             
x - 6 | x² - 10x + 24
          x² - 6x
          0  - 4x + 24
               -4x - 24
                          0
We can see that our quotient is x - 4, which would be the other factor of x - 6 to get x² - 10x + 24. The answer to your query is x - 4. Hope this helps and have a phenomenal day!