Question

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

Answer 1

let`f(x)=x^3-7x^2+14x-8 `

f(1)=`(1)^3-7(1)^2+14(1)-8=1-7+14-8=0 `

Hence,(x-1) is a factor of (x)  

 

∴ `x^3-7x^2+14x-8=(x-1)(x^2-6x+8) `

                          ` =(x-1)(x^2-2x-4x+8)`  

                         `  =(x-1)[x(x-2)-4(x-2)] `

                        `  =(x-1)(x-2)(x-4)`