# What factor is common to all the expressions x² – x, 2x² + x – 1, and x² – 1?

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## What factor is common to all the expressions x² – x, 2x² + x – 1, and x² – 1?

A. x

B. x – 1

C. no common factor

D. x + 1

C

## DETAILS…

To resolve this, we would have to factorize each expression like this:

### First expression:

x² – x = x(x – 1)

### Second expression:

2x² + x – 1

= 2x² + 2x – x – 1

= 2x(x + 1) – 1(x + 1)

= (2x – 1)(x + 1)

At this point the answers is clearly option C, this is because there’s clearly no common factor between the two expressions. no need to solve further since we are time conscious, but to fulfil all righteousness, let us complete it.

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### Third expression:

x² – 1

= x² – x + x – 1

= x(x -1) + 1(x – 1)

= (x – 1)(x + 1)

All three expressions do not have a common factor.

### Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is incorrect.
3. C is correct. no common factor among the three expressions.
4. D is not the correct answer.

## KEY-POINTS…

• Rushing to choose an answer might result in you choosing the wrong option, just resolving only the first two expressions will result in the right option.
• No need to resolve the third expression since there’s no common factor between the first two.
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