Part A: One of the factors of the polynomial function p(x)=2x^4+3x^3−x is (2x−1).
Write p as the product of (2x−1) and another polynomial.

Part B: What are the solutions to the equation p(x)=0? Enter the solutions from least to greatest.

In mathematics, every real-world issue may be transformed into an equation, sometimes in the form of a factor, which must then be expanded to get a solution.

Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.

Given,

p(x)=2x⁴ + 3x³ −x one factor is (2x−1)

To find another factor we divide p(x)=2x⁴ + 3x³ −x by (2x−1)

Then we got remainder as 0 and quotient ( x³ + 2x + 1 )

So,

(2x−1) ( x³ + 2x² + x ) = 0

(2x−1) (x) ( x² + 2x + 1) = 0

(2x−1) (x) (x + 1)² = 0

Now the solution to this

(2x−1) = 0 ⇒ x = 1/2

(2x−1) (x) ( x² + 2x + 1) = 0 ⇒ x = 0

And

(x + 1)² = 0 ⇒ x = -1

Hence, another factor will be x and ( x + 1 )² and the solution will be -1, 0, and 1/2.

For more information about the expansion

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Part A: One of the factors of the polynomial function p(x)=2x^4+3x^3−x is (2x−1). Write p as the product of (2x−1) and another polynomial. Part B: What are the solutions to the equation p(x)=0? Enter the solutions from least to greatest.

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What is expansion?

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Part A: One of the factors of the polynomial function p(x)=2x^4+3x^3−x is (2x−1).
Write p as the product of (2x−1) and another polynomial.

Part B: What are the solutions to the equation p(x)=0? Enter the solutions from least to greatest.