What substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation?

The substitution is

Step-by-step explanation:

We have the 8th degree polynomial equation

To rewrite the equation as a quadratic function, take the common factor of the term x with the smallest exponent, in this case it is .

Now make a change of variable

.

So rewriting the equation in terms of u, we have:

Now the initial equation became a quadratic equation

Factoring is left:

and

and

substitution should be p =  x⁴

Step-by-step explanation:

It is given that,

x⁸ -  3x⁴ + 2 = 0

we can rewrite the equation,

(x⁴)² - 3x⁴ + 2 =0

To find the substitution

Here we can see that x⁴ is common in two terms of the given equation

we can substitute p instead of x⁴, the equation becomes,

p² - 3p +2 = 0

Therefore substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation is p =  x⁴