Question

(x - 1) is a factor of the following, what are the remaining 2 factors:

Answer 1

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)