Perform the operation(s) and simplify completely. x3−2x2+1+3x5−12x4+21x2x2−4x (1 point) Responses −2x3−2x2+7x+1 negative 2 x cubed minus 2 x squared plus 7 x plus 1 - no response given 4x3−9x+1 4 x cubed minus 9 x plus 1 - no response given 4x3−2x2−7x+1 4 x cubed minus 2 x squared minus 7 x plus 1 - no response given 4x3−2x2+7x+1

Answer 1

To simplify the expression \(x^3 - 2x^2 + 1 + 3x^5 - 12x^4 + 21x^2 - 4x\), we can first rearrange the terms in descending order of the powers of \(x\):

\[ 3x^5 - 12x^4 + x^3 + (-2x^2 + 21x^2) + (-4x) + 1 \]

Now, we can combine like terms:

1. The \(x^5\) term: \(3x^5\)
2. The \(x^4\) term: \(-12x^4\)
3. The \(x^3\) term: \(x^3\)
4. The \(x^2\) terms: \(-2x^2 + 21x^2 = 19x^2\)
5. The \(x\) terms: \(-4x\)
6. The constant term: \(1\)

Putting it all together, we have:

\[ 3x^5 - 12x^4 + x^3 + 19x^2 - 4x + 1 \]

The fully simplified expression is:

\[ 3x^5 - 12x^4 + x^3 + 19x^2 - 4x + 1 \]

None of the provided answer choices match, as they seem to be lower degree polynomials. Please check the original expression for any typos or errors.