You haven't made it clear how big integers can be and still be small. The following code can easily be modified as needed

```
R.<x>=ZZ[] #ring of polynomials with integral coefficients
f = R.random_element(2) #choose polynomial from the ring with degree at most 2
L = f.list() #get the coefficients
while L[2] != 1 or abs(L[1])>9 or abs(L[0])>10 or f.is_irreducible() == False:
f = R.random_element(2)
L = f.list()
print(f)
```

L[2] is the coefficient of x^2, so we insist that if it isn't 1 then we throw the polynomial away. We also throw the polynomial away if the coefficient of x in absolute value is >9 or the constant (in absolute value) is >10 or the polynomial is not irreducible.

There's probably a less clunky way to do it but this works.

EDIT: following rburing comment below will mean not having to throw out so many polynomials for not being monic.

```
R.<x>=ZZ[] #ring of polynomials with integral coefficients
poly = R.random_element(1) #choose polynomial from the ring with degree at most 1
f = x^2+poly
L = f.list() #get the coefficients
while abs(L[1])>9 or abs(L[0])>10 or f.is_irreducible() == False:
poly = R.random_element(1)
f = x^2+poly
L = f.list()
print(f)
```