now determine the quadritic factor. x^3+8x^2+17x+10

The given polynomial x^3 + 8x^2 + 17x + 10 can be factored by grouping as follows:

x^3 + 8x^2 + 17x + 10
= x^2(x + 8) + 1(17x + 10)
= x^2(x + 8) + 1(17x + 10)
= x^2(x + 8) + 1(17x + 10)
= x^2(x + 8) + 1(17x + 10)
= (x^2 + 1)(x + 8)

Therefore, the quadratic factor of x^3 + 8x^2 + 17x + 10 is (x^2 + 1)(x + 8).