To simplify the given expression [tex]\(\left(8 x+x^4\right)+\left(6 x-5 x^3+3 x^4\right)\)[/tex], follow these steps:
1. Rewrite the expression by combining like terms:
[tex]\[
\left(8x + x^4\right) + \left(6x - 5x^3 + 3x^4\right)
\][/tex]
2. Group the terms that are similar (i.e., those that have the same power of [tex]\(x\)[/tex]):
- Combine the constant terms involving [tex]\(x\)[/tex]:
[tex]\[
8x + 6x = 14x
\][/tex]
- Combine the terms involving [tex]\(x^4\)[/tex]:
[tex]\[
x^4 + 3x^4 = 4x^4
\][/tex]
- The term involving [tex]\(x^3\)[/tex] remains as it is:
[tex]\[
-5x^3
\][/tex]
3. Write the expression with the simplified like terms:
[tex]\[
4x^4 - 5x^3 + 14x
\][/tex]
4. Factor the common factor out of the resulting expression, if possible:
Notice that [tex]\(x\)[/tex] is a common factor in all terms:
[tex]\[
x(4x^3 - 5x^2 + 14)
\][/tex]
Therefore, the simplified expression is:
[tex]\[
x(4x^3 - 5x^2 + 14)
\][/tex]
