The Students' Conjectures Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x)

Complete Question:

Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x) They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.

Step-by-step explanation:

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Given

Required

Determine how they can show if the products are the same or not

To do this, we simply factorize each polynomial

For, Polynomial A: We have:

Factor out 4x

Apply difference of two squares on x^2 - 4

For, Polynomial B: We have:

Expand x^2 + x - 2

Factorize:

Factor out x + 2

Factor out 4x

Rearrange

The simplified expressions are:

and  

Hence, both polynomials are equal