if (x - 9) is a factor of (x^{2}-5x - 36), what is the other factor?\n(x - 4)\n(x + 4)\n(x - 6)\n(x + 6)

Explanation:

Step1: Factor the quadratic expression

We use the method of factoring quadratic expressions of the form $ax^{2}+bx + c$. For $x^{2}-5x - 36$, we need to find two numbers that multiply to $ac=-36$ and add up to $b = - 5$. The numbers are $-9$ and $4$ since $(-9)\times4=-36$ and $-9 + 4=-5$. So $x^{2}-5x - 36=(x - 9)(x+4)$.

Answer:

B. $x + 4$