The factors of (x2 + 11x + 30) are (X + 5) and (x + 6)
You want to look for two numbers, when multiplied equal 30, and when added equal 11. Start with factors of 30, and see what they add to: 5+6=11, and 5*6=30.
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x2 + 11x + 30 = 0 (x + 5)(x + 6) = 0 so the roots are -5 and -6
x2 - 11x + 24 = (x - 3)(x - 8)
The actual equation itself is the polynomial. There is no polynomial for it, and your question doesn't really make sense.
It is: x^2 +11x +24 = (x+8)(x+3) when factored
This is the equation we want to factorize: x2 - 11x + 18 And there are two answers (the numbers are the same, but +/- signs are inverted): 1. (x - 2)(x - 9) = x2 - 9x - 2x -(-18) = x2 - 11x + 18 2. (-x + 2)(-x +9) = x2 -9x -2x + 18 = x2 - 11x + 18