Question

Find the quotient and the remainder when (x⁵ + 5x + 3x² + 5x³ + 3) is divided by (x² + 4x + 2).

Answer 1

we have to find the quotient and the remainder when (x⁵ + 5x + 3x² + 5x³ + 3) is divided by (x² + 4x + 2)

solution : here divisor = x⁵ + 5x³ + 3x² + 5x + 3

dividend = x² + 4x + 2

using Euclid division lemma,

x² + 4x + 2) x⁵ + 5x³ + 3x² + 5x + 3(x³ - 4x² + 19x - 65

x⁵ + 4x⁴ + 2x³

.......................................................

- 4x⁴ + 3x³ + 3x²

- 4x⁴ - 16x³ - 8x²

........................................................

19x³ + 11x² + 5x

19x³ + 76x² + 38x

..........................................................

-65x² - 33x + 3

-65x² - 260x - 130

.................................................................

+ 227x + 133

Therefore the quotient is x³ - 4x² + 19x - 65 and remainder is 227x + 133

Answer 2

Answer:

360

Step-by-step explanation:

dividend = x² + 4x + 2

using Euclid division lemma,

x^ 2 +4x+2)x^ 5 +5x^ 3 +3x^ 2 +5x+3(x^ 3 - 4x ^ 2 + 19x - 65

x ^ 5 + 4x ^ 4 + 2x ^ 3

- 4x ^ 4 + 3x ^ 3 + 3x ^ 2 - 4x ^ 4 - 16x ^ 3 - 8x ^ 2

19x ^ 3 + 11x ^ 2 + 5x 19x ^ 3 + 76x ^ 2 + 38x

- 65x ^ 2 - 33x + 3 -65x²-260x -

130

+ 227x +

133