Alright! Let's add the two given polynomials step-by-step.
The given polynomials are:
1. [tex]\( 10x^4 - 8x^3 + 3x \)[/tex]
2. [tex]\( -6x^4 - 5x^3 - 4 \)[/tex]
To add these polynomials, we need to combine like terms. Let's line them up according to their respective powers of [tex]\(x\)[/tex]:
[tex]\[
\begin{aligned}
&\phantom{+} 10x^4 - 8x^3 + 0x^2 + 3x + 0 \\
&+ (-6x^4 - 5x^3 + 0x^2 + 0x - 4)
\end{aligned}
\][/tex]
Now, we add the coefficients of the terms with like powers of [tex]\(x\)[/tex]:
1. For [tex]\(x^4\)[/tex]:
[tex]\[
10 + (-6) = 4
\][/tex]
2. For [tex]\(x^3\)[/tex]:
[tex]\[
-8 + (-5) = -13
\][/tex]
3. For [tex]\(x^2\)[/tex]:
[tex]\[
0 + 0 = 0
\][/tex]
4. For [tex]\(x\)[/tex]:
[tex]\[
3 + 0 = 3
\][/tex]
5. For the constant term:
[tex]\[
0 + (-4) = -4
\][/tex]
Putting it all together, the resulting polynomial after adding the two given polynomials is:
[tex]\[
4x^4 - 13x^3 + 0x^2 + 3x - 4
\][/tex]
So, the final result is:
[tex]\[
4x^4 - 13x^3 + 3x - 4
\][/tex]
