Question

by the remainder theorem find the remainder when, p ( x) = 4x^3-3x^2+2x-5 is divided by g(x)= 1-2x ( please show the solution )​

Answer 1

Answer:

The answer is -29/4

Step-by-step explanation:

4(-1/2)^3=-4/8=-1/2

-3(-1/2)^2=-3/4

2(-1/2)=-2/2=-1

-5

so,- 1/2 - 3/4 - 1 - 5

    -2-3-24/4

    -29/4

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Answer 2

Remainder is -17/4.

Given:

• $p(x) = 4 {x}^{3} - 3 {x}^{2} + 2x - 5$ and
• $g(x) = 1 - 2x$

To find:

• Find the remainder when p(x) is divided by g(x), using remainder theorem.

Solution:

Remainder Theorem: If p(x) is divided by g(x)=(x-a), then remainder is given by p(a).

Step 1:

Put g(x)= 0.

$1 - 2x = 0$

or

$2x = 1$

or

$\bf x = \frac{1}{2}$

Step 2:

Put x= 1/2 in p(x).

$p \left( \frac{1}{2} \right ) = 4 {\left( \frac{1}{2} \right )}^{3} - 3 {\left( \frac{1}{2} \right )}^{2} + 2\left( \frac{1}{2} \right ) - 5$

or

$= 4 {\left( \frac{1}{8} \right )} - 3 {\left( \frac{1}{4} \right )} + 2\left( \frac{1}{2} \right ) - 5$

or

$= \frac{1}{2} - \frac{3}{4} +1 - 5$

or

$= \frac{1}{2} - \frac{3}{4} - 4$

or

$= \frac{2 - 3 - 16}{4}$

or

$\bf p \left( \frac{1}{2} \right ) = - \frac{17}{4}$

Thus,

Remainder is -17/4.

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