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