03-02 Sample Quiz - Polynomial Identities

Name:

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Factor.

a.		c.
b.		d.

Which of the below is a factor of

a.		c.
b.		d.

Vincent is trying to create a polynomial identity.
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Step 0: Original Statement.

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Step 1: Expand the binomial expression

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Step 2: Add which is equivalent to adding zero.

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Step 3: Rearrange the order of the terms.

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Step 4: Factor the first 3 terms

and combine terms.

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Step 5: Rewrite the last term as a square.

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Are each of his steps valid? If not, in which step is there an error?

a.	All of Vincent’s steps are valid.
b.	Vincent didn’t correctly expand the binomial in Step 1.
c.	Vincent can’t just add to the expression in Step 2.
d.	Vincent factored incorrectly the terms in Step 4.

Factor.

a.		c.
b.		d.

Jessica was trying to prove the polynomial identity:
x²+ y² = (x+yi) (x– yi)
She made an error because the last step isn’t equivalent.
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Step 0: Original Statement.

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Step 1: Expand the RIGHT side using the FOIL technique.

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Step 2: Combine like terms on the RIGHT side.

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On which step did she potentially make an algebraic error?

a.	Jessica didn’t expand correctly in Step 1.
b.	Jessica incorrectly combined the terms in Step 2.
c.	It is impossible to prove because the original identity is false.

Which of the below is a binomial factor of the polynomial shown?

a.		c.
b.		d.