Question

how many times is -2 a factor of the following
x^3+5x^2+8x+4

Answer 1

Use long-division to divide the original polynomial by x+2, we obtain:

\[x^3 + 5x^2 + 8x + 4 = (x+2)(x^2 + 3x+2)\]

Long-division again, we can factor more

\[x^2 + 3x + 2 = (x+2)(x+1)\]

Conclusion: There are twice times at which -2 is a solution of the original polynomial