Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Factor completely and then place the factors in the proper location on the grid.

x 2 - 5x - 14

Answer 1

(x + 2)(x - 7)

That's your answer!!

Answer 2

The factors are ⇒ (x - 7)(x + 2)

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)