What number should be added to 3x 3 - 5x 2 + 6x so that when resulting polynomial is divided by x - 3, the remainder is 8 ?

Let number to be added be a. ∴ Polynomial = 3x 3 - 5x 2 + 6x + a x - 3 = 0 ⇒ x = 3 On substituting x = 3 in 3x 3 - 5x 2 + 6x + a, remainder = 8. ∴ 3(3) 3 - 5(3) 2 + 6(3) + a = 8 ⇒ 3(27) - 5(9) + 18 + a = 8 ⇒ 81 - 45 + 18 + a = 8 ⇒ a + 54 = 8 ⇒ a = -46 Hence, no. to be added = -46.

Mathematics

What number should be added to 3x³ - 5x² + 6x so that when resulting polynomial is divided by x - 3, the remainder is 8 ?

Factorisation

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Answer

Let number to be added be a.

∴ Polynomial = 3x³ - 5x² + 6x + a

x - 3 = 0 ⇒ x = 3

On substituting x = 3 in 3x³ - 5x² + 6x + a, remainder = 8.

∴ 3(3)³ - 5(3)² + 6(3) + a = 8

⇒ 3(27) - 5(9) + 18 + a = 8

⇒ 81 - 45 + 18 + a = 8

⇒ a + 54 = 8

⇒ a = -46

Hence, no. to be added = -46.

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What number should be added to 3x³ - 5x² + 6x so that when resulting polynomial is divided by x - 3, the remainder is 8 ?

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What number should be added to 3x3 - 5x2 + 6x so that when resulting polynomial is divided by x - 3, the remainder is 8 ?

Factorisation

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