Answer:
The factors are ⇒ (x - 7)(x + 2)
Step-by-step explanation:
* Lets revise the factorization
- If x² + ax + b, the we search for 2 numbers have
product = b and sum = a
∴ (x + m)(x + n), where mn = c and m + n = a
# x² + 5x + 6 = (x + 3)(x + 2) ⇒ (1)
- If x² - ax + b, the we search for 2 numbers have
product = b and sum = a
∴ (x - m)(x - n), where mn = c and m + n = a
# x² - 5x + 6 = (x - 3)(x - 2) ⇒ (2)
- If x² + ax - b, the we search for 2 numbers have
product = b and difference = a
∴ (x + m)(x - n), where mn = c and m - n = a, m > n
# x² + 5x - 6 = (x + 6)(x - 1) ⇒ (3)
- If x² - ax - b, the we search for 2 numbers have
product = b and difference = a
∴ (x - m)(x + n), where mn = c and m - n = a, m > n
# x² - 5x - 6 = (x - 6)(x + 1) ⇒ (4)
* Now solve the problem
# x² - 5x - 14 ⇒ search for 2 numbers their product is 14
and their difference is 5
- The numbers are 7 and 2
∴ x² - 5x - 14 = (x - 7)(x + 2) ⇒ case (4)
