Question

If (x + 9) = 0 is a factor of $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$ , 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)

Let $A=\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$
$\Rightarrow x(x^2-12)-3(2x-14)+7(12-7x)=0$
$\Rightarrow x^3-12x-6x+42+84-49x=0$
$\Rightarrow x^3-67x+126=0$
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.