Question

If x – 9 is a factor of x2 – 5x – 36, what is the other factor? x – 4 x 4 x – 6 x 6

Answer 1

Factors of -36 that add up to -5.

If (x - 9) is a factor, the other factor would be (x + 4).

Answer 2

we have

`x^(2) -5x-36`

equate to zero

`x^(2) -5x-36=0`

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

`x^(2) -5x=36`

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

`x^(2) -5x+6.25=36+6.25`

`x^(2) -5x+6.25=42.25`

Rewrite as perfect squares

`(x-2.5)^(2) =42.25`

`(x-2.5)=(+/-)√(42.25) \\ x1=2.5+6.5=x1=9\\ x2=2.5-6.5=-4`

so

`x^(2) -5x-36=(x+4)*(x-9)`

therefore

the answer is

The other factor is
`(x+4)`