Let a monic quadratic polynomial be written as x2+bx+c and suppose it can be expressed as the product of two linear factors with integer constants.
a. (i) Explain why the sum of the two integer constants equals b and their product equals c.
b. (ii) Using the reasoning from part (i), find two integers whose sum is −7 and product is 12.
c. (iii) Hence, factorise the quadratic expression x2−7x+12.