ANSWER
[tex]13 {x}^{3} - 2 {x}^{2} + 3x + 13[/tex]
EXPLANATION
The first polynomial is
[tex]5 {x}^{3} + 3 {x}^{2} - 5x + 4[/tex]
The second polynomial is
[tex]8 {x}^{3} - 5 {x}^{2} + 8x + 9[/tex]
If we add the two polynomials we obtain,
[tex](5 {x}^{3} + 3 {x}^{2} - 5x + 4) + (8 {x}^{3} - 5 {x}^{2} + 8x + 9)[/tex]
Next we group like terms to obtain,
[tex]5 {x}^{3} + 8 {x}^{3}+ 3 {x}^{2} -5 {x}^{2} - 5x + 8x + 9 + 4[/tex]
We simplify the to obtain,
[tex]13{x}^{3} -2{x}^{2} + 3x + 13[/tex]
This is the sum of the two polynomials in descending powers of
[tex]x[/tex]
Descending means from the highest power to the least.
