Answer:
The factors of given polynomial x =-1 , -2 and x =3
Step-by-step explanation:
Step(i):-
Given the polynomial
f(x) = x³ - 7x -6
put x =-1
f(-1) = (-1 )³- 7(-1) - 6 = -1+7-6=0
(x+1) is a one factor
By using synthetic division
x³ x² x constant
x=-1 ↓ 1 0 -7 -6
↓ 0 -1 1 6
1 -1 -6 0
The polynomial x² - x - 6
Step(ii):-
The factors ( x+1)(x² - x - 6 ) = 0
x = -1 and x² - x - 6 =0
x =-1 and x² - 3x + 2 x - 6 =0
x =-1 and x (x -3) + 2( x-3) =0
x =-1 and (x+2)(x-3) =0
Final answer:-
The factors of given polynomial x =-1 , -2 and x =3
