Answer: Yes.
Explanation:
To see if it is a factor, we can check a few ways. I will show two here. First, we can graph. If the line intercepts the x-axis at x = -10, it is a factor. I have attached a picture of this graph, it does indeed intercept at this point.
A second way is to factor the given function. To do this, we will factor by grouping. This involves "breaking" the terms apart and factoring with different groups. Then, we are left with the same factor being multiplied by two different numbers. This becomes our other factor.
F(x) = 5x³ + 60x² + 109x + 90
F(x) = 5x³ + 10x² + 50x² + 100x + 9x + 90
F(x) = 5x³ + 10x² + 9x + 50x² + 100x + 90
F(x) = x(5x² + 10x + 9) + 10(5x² + 10x + 9)
F(x) = (x + 10)(5x² + 10x + 9)
Yes, (x + 10) is a factor of F(x) = 5x³ + 60x² + 109x + 90 and x = -10 is a solution.