Mark M. answered • 06/15/20

Retired math prof. Very extensive Precalculus tutoring experience.

y = x^{3} + 11x^{2} + 25x + 15

By plugging in -1 for x, we see that -1 is a root (x-intercept), so x + 1 is a factor.

Divide by x + 1 to get y = (x + 1)(x^{2} + 10x + 15)

Setting x^{2} + 10x + 15 equal to zero, we get x = (-10 ± √40) / 2, which are also x-intercepts.

Since the function is of degree 3, there can't be more than 3 x-intercepts.

So, there are exactly 3 x-intercepts.

Jin Y.

thank you so much!06/15/20