Question

If (x + 9) = 0 is a factor of $\begin{vmatrix}x&3&7\\\ 2&x&2\\\ 7&6&x\end{vmatrix} = 0$ , then the other factor is:

• A. (x - 2) (x - 7)
• B. (x - 2) (x - a)
• C. (x + 9) (x - a)
• D. (x + 2) (x + a)

Answer 1

Answer: (A)

(x - 2) (x - 7)

Answer 2

Let $A = \begin{vmatrix}x&3&7\\\ 2&x&2\\\ 7&6&x\end{vmatrix} = 0$ $\Rightarrow \ x (x^2 - 12) - 3 (2x - 14) + 7 (12 - 7x) = 0$ $\Rightarrow \ x^3 - 12x - 6x + 42 + 84 - 49x = 0$ $\Rightarrow \ x^3 - 67x + 126 = 0$ If (x + 9) is a factor of the given equation then $(x + 9) (x^2 - 9x + 14) = 0$ $\Rightarrow \ x^2 - 9x + 14 = 0$ Thus (x - 7) (x - 2) = 0 is the other factor.