Chapter 8, Problem 79SGR

To determine

To factorize the given polynomial

Answer to Problem 79SGR

  $(x^2-4x)(x^2+4x)$

Explanation of Solution

Given:

Polynomial: $x^4-16x^2$

Formula used:

  $a^2-b^2=(a-b)(a+b)$

Calculation:

Consider the given polynomial,

  $\begin{array}{l}\Rightarrow x^4-16x^2\\ $ \Rightarrow x^4-{(4x)}^2$\Rightarrow (x^2-4x)(x^2+4x)[\because a^2-b^2=(a-b)(a+b)]\end{array}$

Conclusion:

Therefore, the factors of the polynomial are $(x^2-4x)(x^2+4x).$