Question

Which of the following should be added to $9x^3+6x^2+x+2$ so that the sum is divisible by (3x+1) ?

• A. -4
• B. -3
• C. -2
• D. -1

Answer 1

Answer: (C)

-2

Let k should be added to the given expression so that the sum is divisible by (3x+1).

Let $f\left(x\right)=9x^3+6x^2+x+2+k$

$f\left(\frac{-1}{3}\right)=0$

$9(\frac{-1}{3}{)}^3+6(\frac{-1}{3}{)}^2-\frac{1}{3}+2+k=0$

$2+k=0$

$k=-2$