Like Terms, Only Stronger

Two terms are like terms when they have the same letter with the same exponent. The terms $x^{2}$ and $2x^{2}$ are like terms. So are $3x$ and $x$. The terms $x^{2}$ and $3x$ are not like terms, because their exponents are different, and adding them cannot change that.

To simplify $x^{2}+3x+2x^{2}+x$, collect each kind of term separately. The $x^{2}$ terms give $x^{2}+2x^{2} = 3x^{2}$. The $x$ terms give $3x+x = 4x$. The result, $3x^{2}+4x$, is a binomial in standard form, and no more terms can be collected.

After you collect the like terms, a polynomial in $x$ has at most one term of each degree. Write those terms from the largest exponent down to get standard form.