Need help factoring roots: Factor. One root has been given.

Question

Factor. One root has been given.

x^4 + 7x^3 - x^2 - 61x - 78 = 0; -4 + √3

Answer 1

Another root is -4-√3

Multiply these two roots together: x²-13.

Divide this into the original equation by long division...or synthetic division if you know that.

You will get a quadratic which can either be factored directly or the factors can be obtained from the quadratic formula.