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# Which of the following is the complete list of roots for the polynomial function f(x) = (x2 + 2x - 15)(x2 + 8x + 17)? A) -5,3 B) -5,3,-4,+I,-4,-i C) -5,3,-4,+I,4+I D) -4+i , -4 -i

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The first of the factors easily. The first quadratic, I want to say. The 2 numbers that add up to +2 and at the same time multiply to -15 and 5, and -3. So these are 2 of the 4 roots we have. The second quadratic is not a factor as well. You need to put that into the quadratic formula to solve. which simplifies to . That gives us a radicand negative, and that's a problem. . Since -1 is equal to i^2, we can rewrite to begin dealing with the negative correctly. . The substitution of -1, i^2 gives us . i^2 is a perfect root of I in it, and the 4 has a perfect square of 2, so that we can simplify more . The 2 in the denominator is reduced by the numerator to give us a final 2 the roots are x = -4 + i, and x = -4 - i. Taking all these roots together, it seems to us that the solution to our problem is the option B (although I think that put a few extra commas to the accident).