How many quadratics of the following forms factorise with integer
coefficients? Here, $b$ is allowed to be any integer (positive,
negative or zero).
$$x^2+bx+10$$
If we knew the value of $b$, how would we go about attempting to
factorise the quadratic?
How might this help us to work out which values of $b$ allow us to
factorise the quadratic?