To find the other factor, we start with the given polynomial:
x² + 2x – 24 = (x + 6)(?)
To find the other factor, we can perform polynomial long division or use the fact that the product of the factors should equal the original polynomial.
We can also expand (x + 6)(x + b) to find b:
(x + 6)(x + b) = x² + (6 + b)x + 6b
By comparing coefficients with the original polynomial:
- Coefficient of x: 6 + b = 2
- Constant term: 6b = -24
From the first equation, we can isolate b:
b = 2 – 6 = -4
Now, using the second equation to check:
6(-4) = -24
This is correct. Thus, the other factor is x – 4.
So, you can summarize that the factors of the polynomial x² + 2x – 24 are (x + 6) and (x – 4).