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.`