Mathematics: Select the correct answer. which is the correct form of for the expression

i dont knowStep-by-step explanation:...

Select the correct answer. which is the correct - id975510, sduquesnay23ocesdcom

Ответ:

deedoe2679

13.03.2022

The correct option is

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.

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

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