Question

Show that (x + 4), (x – 3) and (x – 7) are factors x³ − 6x² − 19x + 84.

Answer 1

Let f(x) =x³ − 6x² − 19x + 84 be the given polynomial 

In order to prove that (x+4), (x-3) and (x-7) are factors of f(x), it is sufficient to prove that f(-4) = 0, f(3) = 0 and f(7) = 0 respectively.

Hence, (x + 4), (x – 3) and (x – 7) are factors of given polynomial x³ − 6x² − 19x + 84.