ANSWER
C.
[tex]3 {x}^{4} - {x}^{3} + 3{x}^{2} + 18x + 4[/tex]
EXPLANATION
We want to multiply;
[tex](3 {x}^{2} + 5x + 1)( {x}^{2} - 2x + 4)[/tex]
We use the distributive property to obtain:
[tex]3 {x}^{2} ( {x}^{2} - 2x + 4) + 5x( {x}^{2} - 2x + 4) + 1( {x}^{2} - 2x + 4)[/tex]
We expand to get:
[tex]3 {x}^{4} - 6 {x}^{3} + 12 {x}^{2} + 5 {x}^{3} - 10 {x}^{2} + 20x + {x}^{2} - 2x + 4[/tex]
Regroup similar terms:
[tex]3 {x}^{4} - 6 {x}^{3} + 5 {x}^{3} + 12 {x}^{2} - 10 {x}^{2} + {x}^{2} + 20x - 2x + 4[/tex]
Combine similar terms:
[tex]3 {x}^{4} - {x}^{3} + 3{x}^{2} + 18x + 4[/tex]
The correct choice is C.
