What is the quotient of (3x4 – 4x2 + 8x – 1) ÷ (x – 2)? 3x3 + 6x2 + 8x + 24 – StartFraction 47 Over x minus 2 EndFraction

3x3 + 6x2 + 8x + 24 + StartFraction 47 Over 3 x Superscript 4 Baseline minus 4 x squared + 8 x minus 1 EndFraction

3x3 + 6x2 + 8x + 24 + StartFraction 47 Over x minus 2 EndFraction

3x3 + 6x2 + 8x + 24 – StartFraction 47 Over 3 x Superscript 4 Baseline minus 4 x squared + 8 x minus 1 EndFraction

The quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24

It can be expressed as 3x³ + 6x² + 8x + 24  + 47 / x - 2

Quotients is the number obtained by dividing one number by another.  

Therefore,

(3x⁴ - 4x² + 8x - 1) ÷ (x - 2)

Using synthetic division:

(3x⁴ - 4x² + 8x - 1) / (x - 2)  = 3x³ + 6x² + 8x + 24 remainder 47

3x⁴ - 4x² + 8x - 1 → Dividend

x - 2 → Divisor

3x³ + 6x² + 8x + 24 → Quotient

47 → Remainder

Therefore, the quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24

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