how do i factor this completely? f(x)=x^3-10x^2+19x+30; x-6

Answer 1

f(x) = x^3-10x^2+19x+30 ; x-6

Synthetic Division method

      6 |  1     -10      19        30

         |   0     6      -24        -30

         |________________________

        1    -4        -5          0

   x -6 is a factor

   x ^2 -4x -5 =0

  x^2 - 5x +x - 5 =0

 x( x - 5) + 1(x - 5)= 0

take out common facyors

 (x - 5)(x + 1) =0

Now this eqations it can be written as

f( x) = ( x-6 )(x-5)(x+1)

The factors of f(x) is ( x-6 )(x-5)(x+1)

Answer 2

f(x) = x^3-10x^2+19x+30 ; x-6

Synthetic Division method

      6 |  1     -10      19        30

         |   0     6      -24        -30

         |________________________

      5 |  1    -4        -5          0

         |  0     5        5

        |________________________

          1     1         0

Now this eqations it can be written as

f( x) = ( x-6 )(x-5)(x-1)

The factors of f(x) is ( x-6 )(x-5)(x-1)

Answer 3

f(x) = x^3-10x^2+19x+30 ; x-6

Synthetic Division method

      6 |  1     -10      19        30

         |   0     6      -24        -30

         |________________________

      5 |  1    -4        -5          0

         |  0     5        5

        |________________________

          1     1         0

Now this eqations it can be written as

f( x) = ( x-6 )(x-5)(x+1)

The factors of f(x) is ( x-6 )(x-5)(x+1)