Chapter 4.4, Problem 6E

To determine

To factor: the polynomial completely.

Answer to Problem 6E

The factorized form is $4k^5-100k^3=4k^3\left(k+5\right)\left(k-5\right)$ .

Explanation of Solution

Given information:

A polynomial is given as

  $4k^5-100k^3$

Calculation:

Consider the given polynomial.

  $4k^5-100k^3$

Take out $4k^3$ common for each term.

  $4k^5-100k^3=4k^3\left(k^2-25\right)$

Now, factorize $\left(k^2-25\right)$ using the polynomial identity $a^2-b^2=\left(a-b\right)\left(a+b\right)$ as shown:

  $\begin{array}{c}\left(k^2-25\right)={\left(k\right)}^2-{\left(5\right)}^2\\ =\left(k+5\right)\left(k-5\right)\end{array}$

Therefore, $4k^5-100k^3=4k^3\left(k+5\right)\left(k-5\right)$