Question

The factors of x³ − 7x + 6 are

Options

• x (x − 6) (x − 1)

• (x² − 6) (x − 1)

• (x + 1) (x + 2) (x + 3)

• (x − 1) (x + 3) (x − 2) 

Answer 1

The given expression to be factorized is  x³ − 7x + 6

This can be written in the form

 x³ − 7x + 6 ` = x^3 - (1 + 6) x + 6`

                    ` = x^3 -x -6x +6`

Take common x from the first two terms and -6from the last two terms. Then we have

  x³ − 7x + 6 = `x(x^2 -1) -6 (x-1)`

                    ` = x{(x)^2 - (1)^2 } -6 (x-1)`

                    ` = x(x+1)(x-1) -6 (x-1)`

Finally, take common(x-1)from the above expression,

  x³ − 7x + 6 = `(x-1){x(x+1) - 6}`

`= (x - 1)(x^2 + x - 6)`

` = (x -1) (x^2 + 3x - 2x - 6)`

` = (x-1){x (x+3) -2 (x+3)}`

` = (x - 1) (x+3) (x-2)`