ANSWER
The simplified polynomial in standard form is
[tex]{x}^{4} - 3 {x}^{3} + 5[/tex]
EXPLANATION
The given expression is
[tex]( {x}^{2} + 1 - 4 {x}^{3} + 3 {x}^{4} ) + ( - {x}^{2} - 2 {x}^{4} + {x}^{3} + 4)[/tex]
We group the terms with the same exponents,
[tex](3 {x}^{4} - 2 {x}^{4} ) + ( - 4 {x}^{3} + {x}^{3} ) + ( {x}^{2} - {x}^{2} ) + (1 + 4)[/tex]
We simplify to obtain,
[tex]{x}^{4} - 3 {x}^{3} + 0 {x}^{2} + 5[/tex]
Since the expression is a polynomial, writing it in standard form means writing the simplified form in descending powers of x.
This will give us,
[tex]{x}^{4} - 3 {x}^{3} + 5[/tex]
