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