Question

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

Answer 1

I would say B for this question

Answer 2

Answer:  The correct option is

(C) $(7x^3-14x^2+28x-55)+\dfrac{124}{x+2}.$

Step-by-step explanation:  We are given to select the correct form of $q(x)+\dfrac{r(x)}{b(x)}$ for the following expression :

$E=\dfrac{7x^4+x+14}{x+2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

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

We have from (i) that

$E\\\\\\=\dfrac{7x^4+x+14}{x+2}\\\\\\=\dfrac{7x^3(x+2)-14x^2(x+2)+28x(x+2)-55(x+2)+124}{x+2}\\\\\\=7x^3-14x^2+28x-55+\dfrac{124}{x+2}\\\\\\=q(x)+\dfrac{r(x)}{b(x)},$

where,

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

Thus, the required form is

$\dfrac{7x^4+x+14}{x+2}=7x^3-14x^2+28x-55+\dfrac{124}{x+2}.$

Option (C) is CORRECT.