Answer:
The factors are the binomials (x - 7)(x + 2)
Step-by-step explanation:
* Lets explain how to factor a trinomial
- The trinomial ax² ± bx ± c has two factors (x ± h)(x ± k), where
# h + k = -b/a
# h × k = c/a
- The signs of the brackets depends on the sign of c at first then
the sign of b
# If c is positive, then the two brackets have the same sign
# If b is positive , then the signs of the brackets are (+)
# If b is negative then the sign of the brackets are (-)
# If c is negative , then the brackets have different signs
* Lets solve the problem
∵ The trinomial is x² - 5x - 14
∴ a = 1 , b = -5 and c = -14
∵ c is negative
∴ The brackets have different signs
∴ (x - h) (x + k) are the factors of the trinomial
∵ h + k = -5/1
∴ h + k = -5 ⇒ (1)
∵ h × k = -14/1
∴ h × k = -14 ⇒ (2)
- From (1) , (2) we search about two numbers their product is 14 and
their difference is 5 , they will be 7 and 2
∵ 7 × 2 = 14
∵ 7 - 2 = 5
- The sign of b is negative then we will put the greatest number in the
bracket of (-)
∴ h = 7 and k = 2
∴ The brackets are (x - 7)(x + 2)
* The factors are the binomials (x - 7)(x + 2)
