Question

Rewrite the expression (x2 – 21x + 38)/(x + 2) in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.

Answer 1

Given the expression;

`(x^2-21x+38)/(x+2)`

We would divide the expression using synthetic division. We have;

`\begin{gathered} x+2=0 \\ x=-2 \end{gathered}`

So;

Thus, the quotient is;

`q(x)=x-23`

The remainder is;

`r(x)=84`

And the divisor is;

`b(x)=x+2`

Thus;

`(x^2-21x+38)/(x+2)=(x-23)+(84)/(x+2)`

FINAL ANSWER:

`(x-23)+(84)/(x+2)`