When we divide 3t4+5t3−7t2+2t+2 by t2+3t+1, we get 3t2−4t+2.
3t2−4t+2t2+3t+13t4+5t3−7t2+2t+2 3t4+9t3+3t2––––––––––––––––2 −4t3−10t2+2t −4t3−12t2−4t–––––––––––––––––– 2t2+6t+2 2t2+6t+2––––––––––––– 0
Thus, the given statement is true.