Chapter 4.6, Problem 14OE

To determine

To Find: Factor of $x^3+1$

Answer to Problem 14OE

Factor of polynomial $x^3+1=\left(x+1\right)\left(x^2+1-x\right)$

Explanation of Solution

Given information: polynomial $x^3+1$

Formula used: sum of cubes

  $a^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right)$

Calculation:

polynomial $x^3+1$

sum of cubes

  $a^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right)$

Here $a=x,b=1$

Then

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