Question

Find the remainder when the polynomial 2x3 –2 x2 + x –1 is divided by (2x—1).

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer:

The remainder of the polynomial $2x^3-2x^2+x-1$ when divide by $(2x-1)$ is $-\frac{3}{4}$.

Step-by-step explanation:

Factor remainder theorem,

If $p(x)$ is a polynomial of degree $n$ and $a$ is zero of the the polynomial, then $(x-a)$ divides the polynomial $p(x)$ such that the remainder of polynomial is the value of $p(a)$.

Step 1 of 2

Consider the polynomial as follows:

$p(x)=2x^3-2x^2+x-1$

It is given that $(2x-1)$ divides the polynomial $p(x)$.

⇒ $2x-1=0$

⇒ $2x=1$

⇒ $x=\frac{1}{2}$ is the zero of the polynomial $p(x)$.

Step 2 of 2

By Factor Remainder theorem,

$p(1/2)$ is the remainder of $p(x)$.

Substitute the value $\frac{1}{2}$ for $x$ in the polynomial $p(x)$ as follows:

$p(\frac{1}{2} )=2\left(\frac{1}{2}\right)^3-2\left(\frac{1}{2}\right)^2+\frac{1}{2}-1$

       $=2\times \frac{1}{8}-2\times \frac{1}{4} +\frac{1}{2}-1$

       $=\frac{1}{4}- \frac{1}{2} +\frac{1}{2}-1$

       $=\frac{1}{4}-1$

$p(\frac{1}{2} )=- \frac{3}{4}$

Therefore, the remainder of the polynomial $2x^3-2x^2+x-1$ when divide by $(2x-1)$ is $-\frac{3}{4}$.

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