How do you factor the trinomial x2+3x+2?

1 Answer
Kaoutar Q.
Mar 8, 2016

Find the roots by calculating the discriminant, you'll find that
x2+3x+2=(x+1)(x+2)

Explanation:

The discriminant of the quadratic polynomial p(x)=ax2+bx+c is D=b2−4ac

When D>0 , p(x) has two distinct real roots :
x1=−b+√D2a and x2=−b−√D2a
and p(x)=(x−x1)(x−x2)

When D=0, p(x) has two coincident real roots
x1=x2=−b2a
so p(x)=(x−x1)2

When D=0, p(x) has no real roots, but two distinct complex roots
z{1,2}=−b±i√−D2a=−b±i√4ac−b22a.

the discriminant of your trinomial p(x)=x2+3x+2 is D=32−4⋅2=1
D>0 means you'll have two distinct real roots :
x=−1andx=−2
therefore : p(x)=(x+1)(x+2)

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

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