Which of the following polynomials is 3x3(x−1)+x(x−1)

Question

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