How to factor quadratic with a leading coefficient?

One method is called the ac method:-

For  example  factor

3x^2 + 2x - 21

ac ( first coefficient times the last) = 3*21 = -63

now we need to find 2 factors of -63 which add up to the coefficient of x  ( + 2):-

+9 and - 7 look good so we can write the original expression as:-

3x^2 + 9x - 7x - 21

Factor by grouping:-

= 3x(x +3) - 7(x + 3)     (  x + 3) is common so:-

= (3x - 7)(x + 3) Answer