which polynomial correctly combines the like terms and puts the given polynomial in standard…

which polynomial correctly combines the like terms and puts the given polynomial in standard form?\n$\frac{1}{3}x + 8x^{4}-\frac{2}{3}x^{2}-x$\n$8x^{4}-\frac{1}{3}x^{2}-x$\n$8x^{4}+\frac{2}{3}x^{2}+\frac{2}{3}x$\n$8x^{4}-\frac{2}{3}x^{2}-\frac{2}{3}x$\n$8x^{4}-\frac{2}{3}x^{2}-x$

which polynomial correctly combines the like terms and puts the given polynomial in standard form?\n$\frac{1}{3}x + 8x^{4}-\frac{2}{3}x^{2}-x$\n$8x^{4}-\frac{1}{3}x^{2}-x$\n$8x^{4}+\frac{2}{3}x^{2}+\frac{2}{3}x$\n$8x^{4}-\frac{2}{3}x^{2}-\frac{2}{3}x$\n$8x^{4}-\frac{2}{3}x^{2}-x$

Answer

Explanation:

Step1: Combine like - terms of $x$

Combine $\frac{1}{3}x$ and $-x$. Since $-x=-\frac{3}{3}x$, then $\frac{1}{3}x - x=\frac{1}{3}x-\frac{3}{3}x=-\frac{2}{3}x$.

Step2: Write the polynomial in standard form

The original polynomial $\frac{1}{3}x + 8x^{4}-\frac{2}{3}x^{2}-x$ after combining like - terms of $x$ becomes $8x^{4}-\frac{2}{3}x^{2}-\frac{2}{3}x$.

Answer:

$8x^{4}-\frac{2}{3}x^{2}-\frac{2}{3}x$ (corresponding to the third option)