## Elementary Linear Algebra 7th Edition

The vectors in $S$ are not linearly independent.
The set $S=\left\{2, x, x+3,3 x^{2}\right\}$ is not a basis for $P_2$ because the vectors in $S$ are not linearly independent. Indeed, one can see that $$x+3=a 2+b x,$$ where $a=\frac{3}{2},b=1$ hence the vectors of $S$ are not linearly independent.