Chapter 4, Problem 9CT

To determine

To find the factors of the polynomial $x^4-8x^2+16$

Answer to Problem 9CT

The factors of the polynomial are $(x+2)$ and $(x-2)$

Explanation of Solution

Given information: $x^4-8x^2+16$

Formula used: $(a+b)(a-b)=a^2-b^2$

Calculation :

Above expression can be written as:

  $\begin{array}{l}{x}^4-8x^2+16\\ =x^4-4x^2-4x^2+16\\ =x^2(x^2-4)-4(x^2-4)\\ $ ={(x^2-4)}^2$$ ={(x+2)}^2{(x-2)}^2$\end{array}$

Hence, the factors of the polynomial are $(x+2)$ and $(x-2)$