Question

Select the correct answer.
Which is the correct form of for the expression

Answer 1

Answer: The correct option is

(C)
`(7x^3-14x^2+28x-55)+(124)/(x+2).`

Step-by-step explanation: We are given to select the correct form of
`q(x)+(r(x))/(b(x))` for the following expression :

`E=(7x^4+x+14)/(x+2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

To find the required expression, we try to divide the numerator by denominator till we get a constant remainder.

We have from (i) that

`E\\\\\\=(7x^4+x+14)/(x+2)\\\\\\=(7x^3(x+2)-14x^2(x+2)+28x(x+2)-55(x+2)+124)/(x+2)\\\\\\=7x^3-14x^2+28x-55+(124)/(x+2)\\\\\\=q(x)+(r(x))/(b(x)),`

where,

`q(x)=7x^3-14x^2+28x-55,~~~~~r(x)=124,~~~~~b(x)=x+2.`

Thus, the required form is

`(7x^4+x+14)/(x+2)=7x^3-14x^2+28x-55+(124)/(x+2).`

Option (C) is CORRECT.