How do you factor the trinomial # x^2 + 3x + 2#?

1 Answer
Mar 8, 2016

Find the roots by calculating the discriminant, you'll find that
#x^2+3x+2 = (x+1)(x+2)#

Explanation:

The discriminant of the quadratic polynomial #p(x)=ax^2+bx+c# is #D=b^2-4ac#

When #D>0# , p(x) has two distinct real roots :
#x1=(-b+sqrtD)/(2a)# and #x2=(-b-sqrt(D))/(2a)#
and #p(x)=(x-x1)(x-x2)#

When #D=0#, p(x) has two coincident real roots
#x1=x2=-b/(2a)#
so #p(x)=(x-x1)^2#

When #D=0#, p(x) has no real roots, but two distinct complex roots
#z{1,2}=\frac{-b \pm i \sqrt {-\D}}{2a}=\frac{-b \pm i \sqrt {4ac-b^2}}{2a}.#

the discriminant of your trinomial #p(x) = x^2+3x+2# is #D=3^2-4*2=1#
#D>0# means you'll have two distinct real roots :
#x = -1 and x=-2#
therefore : #p(x)=(x+1)(x+2)#

Source : https://en.wikipedia.org/wiki/Discriminant