Question

Use factoring to solve the polynomial equationCheck by substitution or by using a graphing utility and identifying x-intercepts

Answer 1

Notice that:

$\begin{gathered} 2x^4=2x^2(x^2), \\ 8x^2=2x^2(4). \end{gathered}$

Therefore, we can rewrite the given equation as follows:

$2x^2(x^2-4)=0.$

Now, notice that:

$4=2^2,$

therefore:

$x^2-4=x^2-2^2=(x-2)(x+2).$

Finally, we get that:

$2x^4-8x^2=2x^2(x-2)(x+2).$

Answer:

$2x^2(x-2)(x+2)=0.$