Factorise 8x⁶+95x³+1

letting u = x^3, you have

8u^2 + 95u + 1
= 1/32 (16u+95-23√17)(16u+95+23√17)
= 1/32 (16x^3+95-23√17)(16x^3+95+23V17)
good luck going further than that!

wolframalpha . com shows the final answer

another factorization is

(2x^2 + 5x + 1)(4x^4 - 10x^3 + 23x^2 - 5x + 1)

To factorize the expression 8x⁶ + 95x³ + 1, we can look for common factors and use a specific factoring technique known as grouping.

Step 1: Look for common factors.
In this case, there are no common factors among the terms of the expression.

Step 2: Group the terms.
We can group the terms by considering a common factor between the first two terms and the last two terms:
(8x⁶ + 95x³) + 1

Step 3: Factor out the common factor from each group.
Taking out x³ as common factor from the first group and 1 as the common factor from the second group, we get:
x³(8x³ + 95) + 1

So the expression can be written as:
x³(8x³ + 95) + 1

This is the factorized form of the given expression, 8x⁶ + 95x³ + 1.