Let's add the two given polynomials step-by-step.
The first polynomial is:
[tex]\[ 5x^3 + 3x^2 - 5x + 4 \][/tex]
The second polynomial is:
[tex]\[ 8x^3 - 5x^2 + 8x + 9 \][/tex]
To add these polynomials, we sum the coefficients of the corresponding powers of [tex]\( x \)[/tex]:
1. For [tex]\( x^3 \)[/tex]:
[tex]\[ 5 + 8 = 13 \][/tex]
So the coefficient of [tex]\( x^3 \)[/tex] in the resulting polynomial is 13.
2. For [tex]\( x^2 \)[/tex]:
[tex]\[ 3 + (-5) = -2 \][/tex]
So the coefficient of [tex]\( x^2 \)[/tex] in the resulting polynomial is -2.
3. For [tex]\( x \)[/tex]:
[tex]\[ -5 + 8 = 3 \][/tex]
So the coefficient of [tex]\( x \)[/tex] in the resulting polynomial is 3.
4. For the constant term:
[tex]\[ 4 + 9 = 13 \][/tex]
So the constant term in the resulting polynomial is 13.
Putting all these together, we get the resulting polynomial:
[tex]\[ 13x^3 - 2x^2 + 3x + 13 \][/tex]
Hence, the sum of the given polynomials is:
[tex]\[ 13x^3 - 2x^2 + 3x + 13 \][/tex]
