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

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)

selected Jan 13, 2013 by liv
+1 vote

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)

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)