Page No 44:
Question 4:
Factorise:
(i) 12x2 − 7x + 1 (ii) 2x2 + 7x + 3
(iii) 6x2 + 5x − 6 (iv) 3x2 − x − 4
(i) 12x2 − 7x + 1
We can find two numbers such that pq = 12 × 1 = 12 and p + q = −7. They are p = −4 and q = −3.
Here, 12x2 − 7x + 1 = 12x2 − 4x − 3x + 1
= 4x (3x − 1) − 1 (3x − 1)
= (3x − 1) (4x − 1)
(ii) 2x2 + 7x + 3
We can find two numbers such that pq = 2 × 3 = 6 and p + q = 7.
They are p = 6 and q = 1.
Here, 2x2 + 7x + 3 = 2x2 + 6x + x + 3
= 2x (x + 3) + 1 (x + 3)
= (x + 3) (2x+ 1)
(iii) 6x2 + 5x − 6
We can find two numbers such that pq = −36 and p + q = 5.
They are p = 9 and q = −4.
Here,
6x2 + 5x − 6 = 6x2 + 9x − 4x − 6
= 3x (2x + 3) − 2 (2x + 3)
= (2x + 3) (3x − 2)
(iv) 3x2 − x − 4
We can find two numbers such that pq = 3 × (− 4) = −12
and p + q = −1.
They are p = −4 and q = 3.
Here,
3x2 − x − 4 = 3x2 − 4x + 3x − 4
= x (3x − 4) + 1 (3x − 4)
= (3x − 4) (x + 1)
