Question

4. Show that (x + 4), (x – 3) and (x - 7) are factors of x-6x2 - 19x +84​

Answer 1

Answer:

hope you understand!

Step-by-step explanation:

let f(x)=x3-6x2-19x+84 be the given polynomial

by the factor theorem,

(x+4),(x-3)and (x-7) are the factors of f(x)

if f(-4), f(3) and f(7) are all equal to zero.

therefore,

f(-4)=(-4)3 - 6(4)2 - 19(-4)+84

      =-64-96+76+84

      =-160+160

      =0

also,

f(3)=(3)3 - 6(3)2 - 19(3)+84

    =27-54-57+84

    =111-111

    =0

and,

f(7)=(7)3 - 6(7)2 - 19(7)+84

    =243-294-133+84

    =427-427

    =0