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.

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step-by-step explanation:

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt