Someone please help I Don't know what to do :)

Question

Given that (x - 4) is a factor of x^5 - x^4-21x^3 + 9x^2 + 108x use polynomial division and factoring to find the roots/zeros of the polynomial

Answer 1

factor out an x, as x=0 is a root or zero

that gives you two zeroes. x=0 and x=4^4-x^3-21x^2+9x +108, using either long or synthetic division, to get

another factor (x^3+3x^2+9x-27)

You now have 3 factors: (x)(x-4)(x^3+3x^2+9x-27) = x^5-x^4-21x^3+9x^2+108x), with zeroes 0 and 4, and potentially 3 more zeroes from the cubic factor. Just trying a few simple integers, like x=1 and x=2 shows a sign change, meaning there is another real zero between 1 and 2. But the other 2 of the 5 total zeroes seem to be imaginary.