Question

Consider the following statements.

1. x – 2 is a factor of x³ – 3x² + 4x – 4.
2. x + 1 is a factor of 2x³ + 4x + 6.
3. x – 1 is a factor of x⁵ + x⁴ – x³ + x² -x + 1.

In these statements

Options

• 1 and 2 are correct

• 1, 2 and 3 are correct

• 2 and 3 are correct

• 1 and 3 are correct

Answer 1

1 and 2 are correct

Explanation:

x – 2 is a factor of x³ – 3x² + 4x – 4

∵ remainder is zero Similarly x + 1 is a factor of 2x³ + 4x + 6

but x – 1 is not a factor of x⁵ + x⁴ – x³ + x² – x + 1

∵ remainder is not zero

∴ Statements 1 and 2 are correct.