Respuesta :
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
What are the Quotients?
Quotients is the number obtained by dividing one number by another.
The given expression is;
(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
The quotient is;
[tex]\rm =\dfrac{3x^4-4x^2+8x-1}{x-2}\\\\=\dfrac{(3x^3 + 6x^2 + 8x + 24)(x-2)}{x-2}\\\\=3x^3 + 6x^2 + 8x + 24[/tex]
Therefore, the quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
learn more on quotients:
brainly.com/question/13515262?
The quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) would be 3x³ + 6x² + 8x + 24.
What are the Quotients?
Quotients are the number that is obtained by dividing one number by another number.
The given expression
(3x⁴ - 4x² + 8x - 1) ÷ (x - 2)
(3x⁴ - 4x² + 8x - 1) / (x - 2) = 3x³ + 6x² + 8x + 24
remainder is 47
Here,
3x⁴ - 4x² + 8x - 1 = Dividend
x - 2 = Divisor
3x³ + 6x² + 8x + 24 = Quotient
47 = Remainder
The quotient is;
(3x⁴ - 4x² + 8x - 1) / (x - 2)
(3x⁴ - 4x² + 8x +24) (x - 2) / (x - 2)
3x³ + 6x² + 8x + 24
Therefore, the quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
learn more about quotients:
brainly.com/question/13515262?
