I assume you mean [tex]24x^4 + 16x^3 + 32x^2 - 16x[/tex]. If that's the case, you need to find the GCD of the coefficients, which in this case is 8. Then, we can say that:
[tex]24x^4 + 16x^3 + 32x^2 - 16x = 8(\frac{24x^4}{8} + \frac{16x^3}{8} + \frac{32x^2}{8} - \frac{16x}{8})\\\\8(3x^4 + 2x^3 + 4x^2 - 2x)[/tex]
Notice how every element inside the parentheses is multiplied by x. Therefore,
[tex]8(3x^4 + 2x^3 + 4x^2 - 2x) = 8x(3x^3 + 2x^2 + 4x - 2)[/tex]
So the common term is 8x.
