Chapter 4.5, Problem 18WE

To determine

To factor thepolynomial.

Answer to Problem 18WE

The value of polynomial is $\left(2p+1\right)\left(4p^2-2p+1\right)$ .

Explanation of Solution

Given information:

  $8p^3+1$

Calculation:

The polynomial can be obtained as

  $\begin{array}{l}8p^3+1\\ ={\left(2p\right)}^3+{\left(1\right)}^3\left[\text{use sum and differnce of cubes}\right]\\ =\left(2p+1\right)\left(4p^2-2p+1\right)\left[\text{since},\left(a^3+b^3\right)=\left(a+b\right)\left(a^2-ab+b^2\right)\right]\end{array}$

Hence,

The value of polynomial is $\left(2p+1\right)\left(4p^2-2p+1\right)$ .