Chapter 4.3, Problem 3E

To determine

To write: the polynomial divisor, dividend, and quotient functions represented by the synthetic division shown at the right.

Answer to Problem 3E

The divisor is $x+3$ .

The dividend is $x^3-2x^2-9x+18$ .

The quotient is $x^2-5x+6$ .

Explanation of Solution

Given information:

The synthetic division is,

  $\begin{array}{ccccc}-3& 1& -2& -9& 18\\ & & -3& 15& -18\\ & 1& -5& 6& 0\end{array}$

Calculation:

The value left to the vertical bar is $-3$ , so $k=-3$ and divisor is

  $\begin{array}{c}x-k=x-\left(-3\right)\\ =x+3\end{array}$

Thus, the divisor is $x+3$ .

The four numbers in top row represents the coefficient of dividend.

  $x^3\left(1\right)+x^2\left(-2\right)+x\left(-9\right)+18=x^3-2x^2-9x+18$

Thus, the dividend is $x^3-2x^2-9x+18$ .

The first three numbers in bottom row represents the coefficient of quotient.

  $x^2\left(1\right)+x\left(-5\right)+6=x^2-5x+6$

Thus, the quotient is $x^2-5x+6$ .