Question

Find trinomial (quadratic expression), given below, find whether it is factorisable or not. Factorise, if possible.
x² - 3x - 54

Answer 1

Given expression : x² - 3x - 54
Comparing with ax² + bx + c, we get a = 1, b = -3, and c = - 54
∴ b² - 4ac = (-3)² - 4(1)(-54) = 9 + 216 = 225, which is a perfect square.
∴ x² - 3x - 54 is factorisable.
Now, x² - 3x - 54 = x² - 9x + 6x - 54
= x( x - 9 ) + 6( x - 9 )
= ( x - 9 )( x + 6 )