Question

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

Answer 1

Answer:

The factors are $(x-7)$  and  $(x+2)$

Step-by-step 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

$(x-2.5)^{2}=20.25$

$(x-2.5)=(+/-)\sqrt{20.25}$

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

$x=2.5(+/-)4.5$

$x=2.5+4.5=7$

$x=2.5-4.5=-2$

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)

Answer 2

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