Question

Factor completely and then place the factors in the proper location on the grid. x^2 - 5x - 14

Answer 1

`x^2 - 5x - 14=\\ x^2+2x-7x-14=\\ x(x+2)-7(x+2)=\\ (x-7)(x+2)`

Answer 2

The factors are
`(x-7)` and
`(x+2)`

Explanation:

we have

`x^(2) -5x-14`

To find the factors equate the equation to zero

`x^(2) -5x-14=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`x^(2) -5x=14`

Complete the square. Remember to balance the equation by adding the same constants to each side

`x^(2) -5x+6.25=14+6.25`

`x^(2) -5x+6.25=20.25`

Rewrite as perfect squares

`(x-2.5)^(2)=20.25`

`(x-2.5)=(+/-)√(20.25)`

`(x-2.5)=(+/-)4.5`

`x=2.5(+/-)4.5`

`x=2.5+4.5=7`

`x=2.5-4.5=-2`

therefore

`x^(2) -5x-14=(x-7)(x+2)`

using a graphing tool see the attached figure

The factors of the quadratic equation are the x-intercepts (values of x when the value of the function is equal to zero)