Q.4. Factorise:

(i) 12x2 + 7x + 1

(ii) 2x2 + 7x + 3

(iii) 6x2 + 5x - 6

(iv) 3x2 - x - 4

Solution:

Using midterm splitting for all the cases, we have,

(i) 12x2 + 7x + 1

=12x2 - 4x - 3x+ 1

= 4x (3x - 1) - 1 (3x - 1)

= (3x - 1) (4x - 1)

(ii) 2x2 + 7x + 3

= 2x2 + 6x + x + 3

= 2x (x + 3) + 1 (x + 3)

= (x + 3) (2x + 1)

(iii) 6x2 + 5x - 6

= 6x2 + 9x - 4x - 6

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

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

(iv) 3x2 - x - 4

= 3x2 - 4x + 3x - 4

= x (3x - 4) + 1 (3x - 4)

= (3x - 4) (x + 1)