The remainder obtained when 8x4 + 14x3 – 2x2 + 7x – 8 is divided b

1.	The remainder obtained when 8x4 + 14x3 – 2x2 + 7x – 8 is divided by 4x2 + 3x – 2 is: 1. 8x – 62. 8x + 63. 14x + 104. 14x – 10
Answer» Correct Answer - Option 4 : 14x – 10 Given: Divivdend = 8x4 + 14x3 – 2x2 + 7x – 8, Divisor = 4x2 + 3x – 2 Concept Used: Deducing given equation in multiple of divisor, we can easily determine remainder Calculation: On deducing given equation ⇒ 8x4 + 14x3 – 2x2 + 7x – 8 ⇒ 8x4 + 6x3 - 4x2 + 8x3 + 2x2 + 7x – 8 ⇒ (4x2 + 3x – 2) × 2x² + 8x3 + 2x2 + 7x – 8 ⇒ [(4x2 + 3x – 2) × 2x²]+ [(4x2 + 3x – 2) × 2x] - 4x² + 11x - 8 ⇒ [(4x2 + 3x – 2) × 2x2 ]+ [(4x2 + 3x – 2) × 2x] + [(4x2 + 3x – 2) × -1] + 14x - 10 ∴ Required remainder = 14x - 10

The remainder obtained when 8x4 + 14x3 – 2x2 + 7x – 8 is divided by 4x2 + 3x – 2 is: 1. 8x – 62. 8x + 63. 14x + 104. 14x – 10

Answer» Correct Answer - Option 4 : 14x – 10

Given:

Divivdend = 8x4 + 14x3 – 2x2 + 7x – 8, Divisor = 4x2 + 3x – 2

Concept Used:

Deducing given equation in multiple of divisor, we can easily determine remainder

Calculation:

On deducing given equation

⇒ 8x4 + 14x3 – 2x2 + 7x – 8

⇒ 8x4 + 6x3 - 4x2 + 8x3 + 2x2 + 7x – 8

⇒ (4x2 + 3x – 2) × 2x² + 8x3 + 2x2 + 7x – 8

⇒ [(4x2 + 3x – 2) × 2x²]+ [(4x2 + 3x – 2) × 2x] - 4x² + 11x - 8

⇒ [(4x2 + 3x – 2) × 2x2 ]+ [(4x2 + 3x – 2) × 2x] + [(4x2 + 3x – 2) × -1] + 14x - 10

∴ Required remainder = 14x - 10

Discussion

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