Question

Find trinomial (quadratic expression), given below, find whether it is factorisable or not. Factorise, if possible.
x(2x - 1) - 1 

Answer 1

Given expression : x(2x - 1) - 1 
Now , x(2x - 1) - 1 = 2x² - x - 1
Comparing with ax² + bx + c, we get a = 2, b = - 1, and c = - 1
∴ b² - 4ac = (- 1)² - 4(2)(-1) = 1 + 8 = 9, which is a perfect square.
∴ 2x² - x - 1 is factorisable.
Now, 2x² - x - 1 = 2x2 - 2x + x - 1
                          = 2x( x - 1 ) + 1( x - 1 )
                          = ( 2x + 1 )( x - 1 )