Which of the binomials below is a factor of this trinomial?

22-5x-14

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)