Answer:
[tex]\huge\boxed{2x^4 + 8x^3 + x^2 + 3x}[/tex]
Step-by-step explanation:
When we multiply a polynomial by a specific monomial, all terms in the polynomial get multiplied by the monomial.
So we can do this by term.
[tex]2x^3 \cdot x[/tex]
Multiplying x by x to the something power will just increase the exponent on the x term by one (since powers are just x multiplied by itself). This means the exponent here will increase by 1, so this becomes [tex]2x^4[/tex].
Same logic applies to the second term: [tex]8x^2[/tex], raise the exponent by one, [tex]8x^3[/tex].
For the third term, if there is no exponent on a term you can assume it's exponent is 1 (so [tex]x^1[/tex] in this case - as [tex]x^1=x[/tex]). Again, using the same logic, this turns into [tex]x^2[/tex].
For the last term, when we multiply a constant by a variable, we get a term with a variable and a coefficient - the constant becomes the coefficient and the variable stays the variable. Therefore, [tex]3 \cdot x = 3x[/tex].
Adding these terms all together gets us [tex]2x^4 + 8x^3 + x^2 + 3x[/tex].
Hope this helped!
