Question

Which of the following polynomials is 3x3(x−1)+x(x−1)
in standard form?(1 point)
Responses

3x4−3x3+x2−x
3 x superscript 4 baseline minus 3 x cubed plus x squared minus x

−3x4−3x3−x2−x
negative 3 x superscript 4 baseline minus 3 x cubed minus x squared minus x

3x4+3x3+x2+x
3 x superscript 4 baseline plus 3 x cubed plus x squared plus x

3x6−6x5+4x4

Answer 1

To put the polynomial \(3x^3(x-1) + x(x-1)\) in standard form, we can simplify each term first.

1. **Distributing \(3x^3(x-1)\):**
\[
3x^3(x - 1) = 3x^4 - 3x^3
\]

2. **Distributing \(x(x-1)\):**
\[
x(x - 1) = x^2 - x
\]

Now we add these two results together:
\[
3x^4 - 3x^3 + x^2 - x
\]

Next, we can organize it in standard form, which is typically written in descending order of degrees:
\[
3x^4 - 3x^3 + x^2 - x
\]

Thus, the polynomial in standard form is:
\[
3x^4 - 3x^3 + x^2 - x
\]

The correct response is:
**3x⁴ − 3x³ + x² − x**