Answer :
To simplify the polynomial
[tex]$$
4x^3 + 9 - 3x^2 + 7x - 2x^3 - 5 - 6x^2,
$$[/tex]
we first group the like terms.
1. Group the cubic terms ([tex]$x^3$[/tex]):
[tex]$$
4x^3 - 2x^3 = 2x^3.
$$[/tex]
2. Group the quadratic terms ([tex]$x^2$[/tex]):
[tex]$$
-3x^2 - 6x^2 = -9x^2.
$$[/tex]
3. The linear term ([tex]$x$[/tex]) is present only as:
[tex]$$
7x.
$$[/tex]
4. Group the constant terms:
[tex]$$
9 - 5 = 4.
$$[/tex]
Combining all the collected like terms, the simplified expression is:
[tex]$$
2x^3 - 9x^2 + 7x + 4.
$$[/tex]
Thus, the answer is:
[tex]$$
\boxed{2x^3 - 9x^2 + 7x + 4}.
$$[/tex]
[tex]$$
4x^3 + 9 - 3x^2 + 7x - 2x^3 - 5 - 6x^2,
$$[/tex]
we first group the like terms.
1. Group the cubic terms ([tex]$x^3$[/tex]):
[tex]$$
4x^3 - 2x^3 = 2x^3.
$$[/tex]
2. Group the quadratic terms ([tex]$x^2$[/tex]):
[tex]$$
-3x^2 - 6x^2 = -9x^2.
$$[/tex]
3. The linear term ([tex]$x$[/tex]) is present only as:
[tex]$$
7x.
$$[/tex]
4. Group the constant terms:
[tex]$$
9 - 5 = 4.
$$[/tex]
Combining all the collected like terms, the simplified expression is:
[tex]$$
2x^3 - 9x^2 + 7x + 4.
$$[/tex]
Thus, the answer is:
[tex]$$
\boxed{2x^3 - 9x^2 + 7x + 4}.
$$[/tex]
