# How do you factor #5x^2 + 30x + 50#?

##### 1 Answer

#### Explanation:

Notice that all of the terms are divisible by

#5x^2+30x+50 = 5(x^2+6x+10)#

The quadratic factor

This has discriminant

#Delta = b^2-4ac = 6^2-(4*1*10) = 36 - 40 = -4#

Since this is negative, this quadratic has no Real zeros and no linear factors with Real coefficients.

We can factor it with Complex coefficients, which we can do by completing the square and using the difference of squares identity:

#A^2-B^2 = (A-B)(A+B)#

with

#x^2+6x+10#

#=(x+3)^2-9+10#

#=(x+3)^2+1#

#=(x+3)^2-i^2#

#=((x+3)-i)((x+3)+i)#

#=(x+3-i)(x+3+i)#

So putting it all together:

#5x^2+30x+50 = 5(x+3-i)(x+3+i)#