Answer:
- 11 or - 15
Step-by-step explanation:
Factorise
x² - 13x + 42
Consider the factors of the constant term (+ 42) which sum to give the coefficient of the x- term (- 13)
The factors are - 6 and - 7, since
- 6 × - 7 = + 42 and - 6 - 7 = - 13, thus
x² - 13x + 42 = (x - 6)(x - 7)
compare to (x + A)(x + B)
A = - 6, B = - 7
thus 3A - B = 3(- 6) - (- 7) = - 18 + 7 = - 11
The factors may also be expressed as (x - 7)(x - 6)
with A = - 7 and B = - 6, then
3A - B = 3(- 7) - (- 6) = - 21 + 6 = - 15
