How do I rewite this polynomial function as a linear factor?

Question

The polynomial function is p(x)=x^4 + 4x^3 -7x^2 - 22x + 24 and has known factors (x+4) and (x-1).

Answer 1

If (x+4) and (x-1) are factors then x=1 and -4 are solutions

If you perform synthetic division first with 1 and next by -4 you are left with x^2+x-6which you can factor to

(x+3)(x-2)so your equation in factored form is

y = (x+4)(x-1)(x+3)(x-2)