Math Snap

STEP 1

Assumptions1. We are given the expression $3 x^{4}+ x^{3}-5 x^{}+4 x^{}+6 x- x-3 x^{4}+7 x^{5}-3 x^{3}$.
. We need to simplify the expression by combining like terms.

STEP 2

First, we need to identify the like terms in the expression. Like terms are terms that have the same variable and exponent.In our expression, the like terms are- $x^{4}$ and $- x^{4}$
- $2 x^{}$ and $- x^{}$
- $-5 x^{2}$ and $4 x^{2}$
- $6 x$ and $-2 x$
- $7 x^{5}$

STEP 3

Now, we add or subtract the coefficients of the like terms to simplify the expression.
For the $x^{}$ terms$$3 x^{} -3 x^{} =0 x^{}$$

STEP 4

For the $x^{3}$ terms$$2 x^{3} -3 x^{3} = -1 x^{3}$$

STEP 5

For the $x^{2}$ terms$$-5 x^{2} +4 x^{2} = -1 x^{2}$$

STEP 6

For the $x$ terms$$6 x -2 x =4 x$$

STEP 7

The $x^{5}$ term remains as it is because it does not have any like terms.
$$7 x^{5}$$

STEP 8

Now, we combine all the simplified terms to get the simplified expression.
$$7 x^{5} +0 x^{4} - x^{3} - x^{2} +4 x$$

We can drop the $x^{4}$ term because it equals zero and does not affect the value of the expression.
So, the final simplified expression is$$7 x^{5} - x^{3} - x^{2} +4 x$$The correct answer is D. $7 x^{5}-x^{3}-x^{2}+4 x$.