Question

If (2x – 3) is a factor of 6x² + x + a, find the value of a. With this value of a, factorise the given expression.

Answer 1

Let 2x – 3 = 0
then 2x = 3
⇒ x = `(3)/(2)`
Substituting the value of x in f(x)
f(x) = 6x² + x + a

`f(3/2) = 6(3/2) + (3)/(2) + a`

= `6 xx (9)/(4) + (3)/(2)`

= `(27)/(2) + (3)/(2) + a`

= `(30)/(2) + a`
= 15 + a
∴ 2x – 3 is the factor
∴ Remainder = 0
∴ 15 + a = 0
⇒ a = –15
Now f(x) will be 6x² + x – 15
Dividing 6x² + x – 15 by 2x – 3, we get

`2x - 3")"overline(6x^2 + x - 15)("3x + 5`
              6x² – 9x
               –    +             
                     10x – 15
                     10x – 15
                     –     +      
                           x       
∴ 6x² + x – 15 = (2x – 3)(3x + 5).