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

$(x-2.5)^{2} =42.25$

$(x-2.5)=(+/-)\sqrt{42.25} \\ x1=2.5+6.5=x1=9\\ x2=2.5-6.5=-4$

so

$x^{2} -5x-36=(x+4)*(x-9)$

therefore

the answer is

The other factor is $(x+4)$