Question

Divide the first polynomial by the second polynomial in each of the following. Also write the quotient and remainder:

(i) 3x² + 4x + 5, x - 2

(ii) 10x² - 7x + 8, 5x - 3

(iii) 5y³ - 6y² + 6y - 1, 5y - 1

(iv) x⁴  - x³ + 5x, x - 1

(v) y⁴ + y², y² - 2

Answer 1

(i) 3x² + 4x + 5, x - 2

Quotient: 3x + 10

Remainder: 25

(ii) 10x² - 7x + 8, 5x - 3

Quotient: 2x - \(\frac{1}{5}\)

Remainder: \(\frac{37}{5}\)

(iii) 5y³ - 6y² + 6y - 1, 5y - 1

Quotient: y² - y + 1

Remainder: 0

(iv) x⁴  - x³ + 5x, x - 1

Quotient: x³ + 5

Remainder: 5

(v) y⁴ + y², y² - 2

Quotient: y² + 1

Remainder: 2