DIVIDING A POLYNOMIAL BY A TRINOMIAL LONG DIVISION

Problem 1 :

(5x⁶ – 16x⁵ – 11x⁴ + 22x³ + 14x² – 4x + 9) ÷ (x² - 4x + 2)

Solution :

Quotient = 5x⁴ + 4x³ - 5x² - 6x

Remainder = 8x + 9

Problem 2 :

(3x⁴ + 15x³ + 3x² - 12x + 4) ÷ (x² + 4x - 2)

Solution :

Quotient = 3x² + 3x - 3

Remainder = 6x - 2

Problem 3 :

(6x⁴ – 30x² + 24) ÷ (2x² – 8)

Solution :

(6x⁴ – 30x² + 24) ÷ (2x² – 8)

Quotient = 3x² – 3

Remainder = 0

Problem 4 :

(3x⁵ + 4x³ – 5x + 8) ÷ (x² + 3)

Solution :

(3x⁵ + 4x³ – 5x + 8) ÷ (x² + 3)

Quotient = 3x³ – 5x

Remainder = 10x + 8

Problem 5 :

(x⁵ + 2x⁴ + x³ – x² – 22x + 15) ÷ (x² + 2x – 3)

Solution :

(x⁵ + 2x⁴ + x³ – x² – 22x + 15) ÷ (x² + 2x – 3)

Quotient = x³ + 4x - 9

Remainder = 8x - 12