Question

x^2- 4x + 24
how to factor?

Answer 1

x 2 − 4 x + 24  is of the form  a x 2 + b x + c  with  a = 1 ,  b = − 4  and  c = 24 .

This has discriminant

Δ = b 2 −4a c = ( − 4 ) 2 − ( 4 × 1 × 24 ) = 16 − 96 = − 80

Since  Δ < 0 ,  x 2 − 4 x + 24 = 0

has 2 complex, non-real roots and  x 2 − 4 x + 24

has no linear factors with real coefficients.

In other words  x 2 − 4 x + 24

is already in simplest terms for real coefficients.