Question

Solve the polynomial equation using division and factoring / the quadratic formula. Write the solution in simplest form. Show all work.

Answer 1

The polynomial is

$\begin{gathered} x^3-8x^2-15x+54=0 \\ \text{and we are dividing it by x-2} \end{gathered}$

Thus, we are left to factorize the quotient to obtain the remaining factors, let's do that

$\begin{gathered} x^2-6x-27 \\ we\text{ try obtain 2 factors that sum to get -6, and multiply to get-27, } \\ \text{the numbers are 3 and -9} \\ x^2+3x-9x-27 \\ x(x+3)-9(x+3) \\ (x+3)(x-9) \end{gathered}$

Thus, the polynomial in its simplest factorized form is;

$(x-2)(x+3)(x-9)$