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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