Determine whether the given binomial is a factor of x^3+13x^2+31x-45

Question

x+5

Answer 1

To check if x+5 is a factor of x^3+13x^2+31x-45, we can use synthetic division.

Using synthetic division:

-5 | 1 13 31 -45
|______ -5 10 -55
1 8 41 -100

The result of the synthetic division is 1x^2 + 8x + 41 - 100/(x+5).

Since the remainder is not equal to zero, x+5 is not a factor of x^3+13x^2+31x-45.