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Question
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
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Solution
Let a be subtracted from 2x2 – 5x,
Dividing 2x2 – 5x by 2x + 1,
`2x+1")"overline(2x^2-5x-a)"(x - 3`
2x2+x
– –
–6x – a
–6x – 3
+ +
–a + 3
Here remainder is (3 – a)
but we are given that remainder is 2.
∴ 3 – a = 2
⇒ –a = 2 – 3 = –1
⇒ a = 1
Hence 1 is to be subtracted.
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