Chapter 8.6, Problem 55PFA

To determine

To determine the factor of an expression.

Answer to Problem 55PFA

  $(x-9)$ or option $\text{(}a\text{)}$

Explanation of Solution

Given:

  $x^2-3x-108$

Calculation:

Consider the given expression,

  $\Rightarrow x^2-3x-108$

Now using middle term factorisation method,

  $\begin{array}{l}\Rightarrow x^2-3x-108\\ \Rightarrow x^2-9x+12x-108\\ \Rightarrow x(x-9)+12(x-9)\\ \Rightarrow (x+12)(x-9)\end{array}$

So the factors of the given expression are $(x+12)(x-9)$ .

Conclusion:

Therefore, the factor is $x-9$ , which is option(a).