Chapter 4.3, Problem 28E

To determine

To find: All the factors of $x^3+7x^2-x-7$ if one of the factors is $x+1$ , using synthetic division.

Answer to Problem 28E

  $\text{The factors are: }\left(x+1\right)\text{ and }\left(x+7\right)$

Explanation of Solution

Given information: $x^3+7x^2-x-7$

Calculation:

Separate coefficients from variables.

  $1\text{ 7 }-1-7$

Take the R coefficient and divide your coefficient from the polynomial.

Given coefficient from binomial: $\pm 1$

  $\begin{array}{l}\underset{\_}{x^3+7x^2-x-7}\\ 1\text{ 7 }-1-7\\ \underset{\_}{\downarrow \text{ 1 8 7 }}\\ 1\text{ 8 7 0}\end{array}$

Combine coefficients to your variables.

  $x^2+8x+7$

Factor the polynomial into two binomials.

  $\text{The factors are: }\left(x+1\right)\text{ and }\left(x+7\right)$