Question

2) Divide (4x - x + 2) by (x + 1) and find remainder. Also find value of polynomial 4r – x+ 2 when r=-1. Compare the two results and write the - relation between remainder and value of the polynomial.​

Answer 1

Answer:

I DON'T NOW THE ANSWER KKKKKKKKKKKKK

Answer 2

Given:

Two polynomials $(4x-x+2)$ and $(x+1)$

To find:

The value of remainder when $(4x-x+2)$ is divided by $(x+1)$.

Value of $4r-x+2$ when $r=-1$

Solution:

The expression $(4x-x+2)$ can be simplified further.

$(4x-x+2)=3x+2$.

For dividing $(3x+2)$ by $(x+1)$, we do the following steps:

$(3x+2)$ is the dividend and $(x+1)$ is the divisor.

Consider the first term in $(3x+2)$, i.e., $3x$. The first term has to be cancelled, hence to obtain $3x$ in the simplifying part, we need to multiply $3$ with $x$ from the divisor, $(x+1)$. Write $3$ as the quotient. Multiply $3$ in the quotient with the first term of divisor, i.e., $x$ to obtain $3x$. Write this $3x$ under the $3x$ in dividend and subtract it to get $0$.

Next, multiply $3$ in the quotient with the second term of divisor, i.e., $1$, to obtain $3$. Write this $3$ under the second term of dividend, i.e., $2$.

Hence, the new expression obtained is $3x+3$ under the dividend. Subtract $3x+3$ from $(3x+2)$ to obtain a remainder $-1$ as shown in the figure.

Thus, the remainder obtained from dividing $(4x-x+2)$ by $(x+1)$ is  $-1$ .

Consider $4r-x+2$. When $r=-1$,

$4(-1)-x+2=-4-x+2=-2-x=-(x+2)$

The polynomial obtained is $-(x+2)$.

Divide this with $(x+1)$ as shown in the second figure. Here, the first term of dividend is $-x$. So, we multiply with $1$ in order to result in $x$ which on adding with $-x$ will be $0$. $1$ is multiplied with $1$ and written under second term of dividend and added with $-2$ to obtain remainder $-1$.

Thus, the remainder obtained from dividing $-(x+2)$ with $(x+1)$ is also $-1$.

On comparing, the same remainders are obtained.

We have the formula,

$Dividend=(Divisor * Quotient)+Remainder$

$(3x+2)=[(x+1)*3]-1$

$-(x+2)=[(x+1)*1]-1$

Remainders obtained are equal on comparing the results and the relation between remainder and value of polynomial is given by:

$(3x+2)=[(x+1)*3]-1$

$-(x+2)=[(x+1)*1]-1$