Question

Rewrite (2x^2+13x+26) / x+4 in the form q(x)+r(x)/b(x) . Then find q(x) and r(x). In the rewritten expression, q(x) is_____and r(x) is______ .

#1 a.)x+a , b.)2x+5 , c.)2x+13
#2 a.)0 , b.)6 , c.)226
ive been stuck on this for 15 mins and i need help plz

Answer 1

The value of q(x) is
`2 x+5`

The value of r(x) is
`6`

Step-by-step explanation:

The given expression is
`(2 x^(2)+13 x+26)/(x+4)`

We need to rewrite the expression in the form of
`q(x)+(r(x))/(b(x))`

Simplifying the expression, we get,

`(2 x^(2)+8 x+5x+26)/(x+4)`

Separating the fractions, we have,

`(2 x^(2)+8 x)/(x+4)+(5 x+26)/(x+4)`

`2 x+(5 x+26)/(x+4)` -----------(1)

Now, we shall further simplify the term
`(5 x+26)/(x+4)` , we get,

`(5 x+26)/(x+4)=(5 x+20)/(x+4)+(6)/(x+4)`

Common out 5 from the numerator, we have,

`(5 x+26)/(x+4)=5+(6)/(x+4)`

Substituting the value
`(5 x+26)/(x+4)=5+(6)/(x+4)` in the equation(1), we get,

`2 x+5+(6)/(x+1)`

Thus, the expression
`(2 x^(2)+13 x+26)/(x+4)=2 x+5+(6)/(x+1)` is in the form of
`q(x)+(r(x))/(b(x))`

Hence, we have,

`q(x)=2 x+5`

`r(x)=6` and

`b(x)=x+4`