How do I factor x^2+4x+20?

Question

Hi! can someone please help me with this question: x^2+4x+20 ?

Answer 1

x^2 + 4x + 20

First, look at the discriminant: b2 - 4ac = 16 - 80 = -64 (negative and therefore not factorable)

Can be solved by completing the square:

x^2 + 4x + 20

x^2 + 4x = -20

x^2 + 4x + 4 = -20 + 4

(x + 2)² = - 16

x + 2 = ±4i

x = -2 ±4i

Answer 2

You cannot factor it over the reals

By quadratic formula, the imaginary solutions are:

[-4 +or- sqrt( 16 - 4*20)]/2 =

[-4 +or- sqrt( 16-80)]/2 =

[-4 +or- sqrt(-64)]/2 =

[-4 +or- 8i]2 =

-2 + or- 4i

So the factors are:

[(x+2) + 4i ][ (x+2) - 4i] =

(x+2)^2 - (-16) =

x^2 + 4x +4 + 16 =

x^2 +4x +20

SO the factored form over the imaginary/complex numbers are:

[(x+2) + 4i ][ (x+2) - 4i]