Question

Show that (x - 1) is a factor of x³ - 7x² + 14x - 8. Hence, completely factorise the above expression.

Answer 1

If (x - 1) is a factor of x³ - 7x² + 14x - 8 then on putting x - 1 = 0
x = 1
f(1) = 0
= 1³ - 7(1)² + 14(1) - 8
= 1 - 7 + 14 - 8 = 0
Hence, x - 1 is one factor.
To find other factors
= x³ - 7x² + 14x - 8
= x²(x - 1) - 6x(x - 1) + 8(x - 1)
= (x - 1) (x² - 6x + 8)
= (x - 1) (x² - 4x - 2x + 8)
= (x - 1) {x(x - 4) - 2(x - 4)}
= (x - 1) (x - 2) (x - 4).