Which of the following are the factors of q³ - q² + 2q - 2?
(q - 1)(2 - q)
(q + 1)(q² + 2)
(q - 1)(2 - q²)
(q - 1)(q² + 2)

Solution:

Given, q³ - q² + 2q - 2

We have to find the factors of the given polynomial.

Factoring polynomials is done in many ways. Let us try taking the common terms out of the first two terms and the last two terms.

q³ - q² + 2q - 2 = q²(q - 1) + 2(q - 1)

= (q² + 2)(q - 1)

Therefore, (q² + 2)(q - 1) are the factors of q³ - q² + 2q - 2.

Example: 

Which of the following are the factors of q⁴ - q³ + 2q² - 2q?

Solution:

Given, q⁴ - q3 + 2q² - 2q

We have to find the factors of the given expression.

q⁴ - q³ + 2q² - 2q = q³(q - 1) + 2q(q - 1)

= (q³ + 2)(q - 1)

Therefore, (q³ + 2)(q - 1) are the factors of q⁴ - q³ + 2q² - 2q.

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Which of the following are the factors of q³ - q² + 2q - 2?

Summary:

The factors of q³ - q² + 2q - 2 are  (q² + 2)(q - 1).