Question

Please help!Use synthetic division and the given fact to solve the fallowing equation. x^3+4x^2-17x-60=0; (x-4)

Answer 1

From the given facts, x-4 is a root of our polynomial, then we can compute the synthetic division of our polynomial by x-4, that is

Let's compute the synthetic division,

then, our division leads to

Now, we can note that the quadratic polynomial can be written as

$x^2+8x+15=(x+3)(x+5)$

Then, our given polynomial is equal to

$x^3+4x^2-17x-60=(x-4)(x+3)(x+5)$

So, we need to solve

$(x-4)(x+3)(x+5)=0$

Therefore, the solutions are

$\begin{gathered} x=4 \\ x=-3 \\ x=-5 \end{gathered}$