Mathematics
What number should be subtracted from x3 + 3x2 - 8x + 14 so that on dividing it by x - 2, the remainder is 10 ?
Factorisation
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Answer
Let number to be subtracted be a.
∴ Polynomial = x3 + 3x2 - 8x + 14 - a
x - 2 = 0 ⇒ x = 2
On substituting x = 2 in x3 + 3x2 - 8x + 14 - a, remainder = 10.
∴ (2)3 + 3(2)2 - 8(2) + 14 - a = 10
⇒ 8 + 3(4) - 16 + 14 - a = 10
⇒ 8 + 12 - 16 + 14 - a = 10
⇒ 18 - a = 10
⇒ a = 18 - 10 = 8.
Hence, no. to be subtracted = 8.
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