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)

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step-by-step explanation: