Answer:
A
Step-by-step explanation:
A trinomial can be factored into two binomials, when the discriminant of the trinomial is greater than or equal to 0.
The discriminant for trinomial [tex]ax^2+bx+c[/tex] is he expression [tex]D=b^2-4ac.[/tex]
Check all options:
A.
[tex]D=3^2-4\cdot 1\cdot 2=9-8=1,[/tex]
then
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}=\dfrac{-3\pm\sqrt{1}}{2}=-2,\ -1.[/tex]
Thus,
[tex]x^2+3x+2=(x-x_1)(x-x_2)=(x-(-2))(x-(-1))=(x+2)(x+1).[/tex]
B.
[tex]D=4^2-4\cdot 1\cdot 5=16-20=-4<0,[/tex]
so this trinomial cannot be factored.
C.
[tex]D=5^2-4\cdot 1\cdot 7=25-28=-3<0,[/tex]
so this trinomial cannot be factored.
D.
[tex]D=6^2-4\cdot 1\cdot 10=36-40=-4<0,[/tex]
so this trinomial cannot be factored.
