Question

Name the remainder for the quotient and describe or show how you found theremainder.(23 - 22 – 17x – 15) = (2x – 5)

Answer 1

Here, dividend is

$f(x)=x^3-x^2-17x-15$

Divisor is (x-5).

Let the quotient be Q(x) and teh remainder be R(x).

By the divison algorithm,

$x^3-x^2-17x-15=(x-5)Q(x)+R(x)$

Now,

$\begin{gathered} f(5)=125-25-85-15 \\ =0 \end{gathered}$

Therefore, there is no remainder by the division algorithm.

Quotient is

$x^2+4x+3$