16x⁴-4x²-4x-1 and 8x³-1
HCF

We have expanded formula of (-4x-1)² = a²+2ab+b².

So, we write the formula in square form as (a+b)².

Since we have a²-b² in step 4. We further write this as (a+b)(a-b). This is the factor formula of a²-b².

As we had two terms in place of in (a+b)(a-b), we multiply the term 'b' with '+' and '-' sign respectively.  

Write the second expression given in the question.

Write the terms in the form of cube.

Write the factor formula of a³-b³) in the form of (a-b)(a²+ab+b²).

Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (4x²+2x+1) are the common factors.

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.