Write 6(x - 5)⁴ + 4(x - 5)² + 6 = 0 in the form of a quadratic by using substitution.

Solution:

Higher polynomial functions can be simplified using the substitution method and further converting to quadratic form.

Let (x - 5)² = t

Thus, the given expression reduces to the form:

⇒ 6t² + 4t + 6 = 0

Thus, the reduced expression for 6(x - 5)⁴ + 4(x - 5)² + 6 = 0 can be written as 6t² + 4t + 6 = 0 in the quadratic expression form.

Write 6(x - 5)⁴ + 4(x - 5)² + 6 = 0 in the form of a quadratic by using substitution.

Summary:

The reduced expression for 6(x - 5)⁴ + 4(x - 5)² + 6 = 0 can be written as 6t² + 4t + 6 = 0 in the quadratic expression form.