Which of the following polynomials is 3x^3(x−1)+x(x−1)
in standard form?(1 point)
Responses
3x^4+3x^3+x2+x
3 x to the 4th power plus 3 x cubed plus x squared plus x - no response given
−3x^4−3x^3−x^2−x
negative 3 x to the 4th power minus 3 x cubed minus x squared minus x - incorrect
3x^6−6x^5+4x^4
3 x to the 6th power minus 6 x to the 5th power plus 4 x to the 4th power - no response given
3x^4−3x^3+x2−x
3 x to the 4th power minus 3 x cubed plus x squared minus x
To simplify the polynomial 3x^3(x-1)+x(x-1), we can distribute the terms.
First, distribute 3x^3 to both terms inside the parentheses:
3x^3 * x - 3x^3 * 1 = 3x^4 - 3x^3
Next, distribute x to both terms inside the parentheses:
x * x - x * 1 = x^2 - x
Now we can combine like terms:
3x^4 - 3x^3 + x^2 - x
Therefore, the polynomial in standard form is 3x^4 - 3x^3 + x^2 - x.
To determine which of the following polynomials is in standard form for the expression 3x^3(x−1)+x(x−1), we need to simplify the expression and rearrange the terms.
First, let's distribute the terms within the parentheses:
3x^3(x−1) = 3x^4 - 3x^3
x(x−1) = x^2 - x
Now, combine the simplified terms:
3x^4 - 3x^3 + x^2 - x
This is the final simplified form of the given expression. Therefore, the polynomial 3x^4 - 3x^3 + x^2 - x is in standard form.