Question

Write the expression in quadratic form, if possible. Otherwise, write not possible.9x^8-21x^4+12

Answer 1

Notice that the exponents of x are multiples of 4: 0, 4 and 8.

We can rewrite x^8 as follows:

$x^8=\left(x^4\right)^2$

Then, one way to write the given expression in quadratic form is:

$9x^8-21x^4+12=9(x^4)^2-21(x^4)+12$

Therefore, the expression in quadratic form is:

$\begin{equation*} 9(x^4)^2-21(x^4)+12 \end{equation*}$