Question

16x⁴-4x²-4x-1 and 8x³-1
HCF​

Answer 1

The student is looking to determine the Highest Common Factor (HCF) of the polynomials 16x⁴-4x²-4x-1 and 8x³-1, which involves factoring each polynomial and identifying the largest common factor. However, without further simplification, we cannot directly compute the HCF.

Step-by-step explanation:

The question asks for the Highest Common Factor (HCF) of two polynomials, 16x⁴-4x²-4x-1 and 8x³-1. To find the HCF of these two polynomials, we would typically factor each polynomial separately and then identify the largest polynomial that is a factor of both original polynomials. However, without further simplification or context provided in the question, we cannot compute the HCF directly. Typically, we use methods like long division or synthetic division to factor polynomials, and common factoring techniques to find common factors.

Answer 2

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.