The zeroes of a polynomial are the X coordinates of the points. Where its graph touches X-axis. Now let us find the points to draw the graph.

So the graph of polynomial x2 + 8x + 15 passes through the points (0, 15), (1, 24), (2, 35), (-1, 8), (-2, 3), (-3, 0) and (-4, -1), (-5, 0)
The adjacent graph intersect the X-axis at – 3 and – 5.
Hence they are zeroes of it.