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# Which of the following are the factors of q^{3} - q^{2} + 2q - 2?

(q - 1)(2 - q)

(q + 1)(q^{2} + 2)

(q - 1)(2 - q^{2})

(q - 1)(q^{2} + 2)

**Solution:**

Given, q^{3} - q^{2} + 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.

q^{3} - q^{2} + 2q - 2 = q^{2}(q - 1) + 2(q - 1)

= (q^{2 }+ 2)(q - 1)

Therefore, (q^{2} + 2)(q - 1) are the factors of q^{3} - q^{2} + 2q - 2.

**Example: **

Which of the following are the factors of q^{4} - q^{3} + 2q^{2} - 2q?

**Solution:**

Given, q^{4} - q3 + 2q^{2} - 2q

We have to find the factors of the given expression.

q^{4} - q^{3} + 2q^{2} - 2q = q^{3}(q - 1) + 2q(q - 1)

= (q^{3} + 2)(q - 1)

Therefore, (q^{3 }+ 2)(q - 1) are the factors of q^{4} - q^{3} + 2q^{2} - 2q.

## Which of the following are the factors of q^{3} - q^{2} + 2q - 2?

**Summary:**

The factors of q^{3} - q^{2} + 2q - 2 are (q^{2 }+ 2)(q - 1).

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