00:01
This problem wants us to form a polynomial whose real zeros and degree are given, and the zeros we're given are negative 5, negative 3, 2, and 3, with degree 4, and we're going to begin building this polynomial by first writing our zeros in the binomial form that that solution would come from when set equal to zero.
00:19
So negative 5 would come from x plus 5, negative 3 would come from x plus 3, positive 2 would come from x minus 2, and then our positive 3 would come from x minus 3.
00:31
And to get this polynomial in standard form, we'll multiply all of our factors together, and since multiplication's order doesn't matter as long as everything gets multiplied together, we're going to first multiply x plus 3 times x minus 3, because that follows the pattern a plus b times a minus b, and the result of a plus b times a minus b is always a squared minus b squared.
00:53
So our x plus 3 times x minus 3 will leave us with x squared minus 9, and now we need to multiply x plus 5 times x minus 2 as well...