Answer:
(x +(-2) ) and ( x+3)
The factors of a given cubic polynomial function are
( x-1) (x -2 ) and (x +3)
Step-by-step explanation:
Step(i):-
Given that x³ - 7x + 6=0
f(x) = x³ - 7x + 6=0
put x=1
f(1) = 1 -7 +6 =0
(x -1 ) is one factor of given polynomial
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) =0
Step(ii):-
The factors of
x² + x - 6=0
x² + 3x -2x - 6=0
x ( x +3 ) - 2( x +3) =0
(x -2 ) ( x+3 ) =0
x = 2 and x =-3
Final answer:-
The factors of a given cubic polynomial function are
( x-1) (x -2 ) and (x +3)
