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Gwar [14]
3 years ago
5

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

lynomial product B: (x2 + x – 2)(4x2 – 8x)
Mathematics
1 answer:
noname [10]3 years ago
3 0

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.

Answer:

A = B

Step-by-step explanation:

<em>See comment for complete question</em>

Given

A: (4x^2 - 4x)(x^2 - 4)

B: (x^2 + x - 2)(4x^2 - 8x)

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:

A: (4x^2 - 4x)(x^2 - 4)

Factor out 4x

A: 4x(x - 1)(x^2 - 4)

Apply difference of two squares on x^2 - 4

A: 4x(x - 1)(x - 2)(x+2)

For, Polynomial B: We have:

B: (x^2 + x - 2)(4x^2 - 8x)

Expand x^2 + x - 2

B:(x^2 + 2x - x - 2)(4x^2- 8x)

Factorize:

B:(x(x + 2) -1(x + 2))(4x^2- 8x)

Factor out x + 2

B:(x -1) (x + 2)(4x^2- 8x)

Factor out 4x

B:(x -1) (x + 2)4x(x- 2)

Rearrange

B: 4x(x - 1)(x - 2)(x+2)

The simplified expressions are:

A: 4x(x - 1)(x - 2)(x+2) and  

B: 4x(x - 1)(x - 2)(x+2)

Hence, both polynomials are equal

A = B

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