Question
Find trinomial $($quadratic expression$),$ given below, find whether it is factorisable or not. Factorise, if possible.$x(2x - 1) - 1$
✓
Answer
Given expression :$ x(2x - 1) - 1$
Now , $x(2x - 1) - 1 = 2x^2 - x - 1$
Comparing with $ax^2 + bx + c$, we get $a = 2, b = - 1$, and $c = - 1$
$\therefore b^2 - 4ac = (- 1)^2 - 4(2)(-1) = 1 + 8 = 9$, which is a perfect square.
$\therefore 2x^2 - x - 1$ is factorisable.
Now, $2x^2 - x - 1 = 2x2 - 2x + x - 1$
$= 2x( x - 1 ) + 1( x - 1 )$
$= ( 2x + 1 )( x - 1 )$
Now , $x(2x - 1) - 1 = 2x^2 - x - 1$
Comparing with $ax^2 + bx + c$, we get $a = 2, b = - 1$, and $c = - 1$
$\therefore b^2 - 4ac = (- 1)^2 - 4(2)(-1) = 1 + 8 = 9$, which is a perfect square.
$\therefore 2x^2 - x - 1$ is factorisable.
Now, $2x^2 - x - 1 = 2x2 - 2x + x - 1$
$= 2x( x - 1 ) + 1( x - 1 )$
$= ( 2x + 1 )( x - 1 )$
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