Answer: option a.
Step-by-step explanation:
To factor a polynomial of degree 2, with the form [tex]ax^{2}+bx+c[/tex], you must find two number whose sum is a and whose product is c. Then:
a) [tex]x^2+3x+2\\(x+1)(x+2)[/tex]
(it can be factored into two binomials)
b) [tex]x^2+4x+5[/tex] cannot be factored into two binomials.
c) [tex]x^2+5x+7[/tex] cannot be factored into two binomials.
d) [tex]x^2+6x+10[/tex] cannot be factored into two binomials.
Therefore, the answer is the option a.
