Question

Show that (x – 2) is a factor of 3x² – x – 10 Hence factorise 3x² – x – 10.

Answer 1

Let x – 2 = 0, then x = 2
Substituting the value of x in f(x),
f(x) = 3x² – x – 10
= 3(2)² – 2 – 10
= 12 – 2 – 10
= 0
∵ Remainder is zero
∴ x – 2 is a factor of f(x)
Dividing 3x² – x – 10 by x – 2, we get

`x - 2")"overline(3x^2 - x - 10)("3x + 5`
           3x² – 6x              
            –   +                 
                   5x – 10
                   5x – 10
                   –   +           
                       x            
∴ 3x2 – x –  10 = (x –  2)(3x + 5).