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