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Question
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
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Solution
Let a be added to 2x3 – 7x2 + 2x dividing it by 2x – 3, then
`2x - 3")"overline(2x^3 - 7x^2 + 2x + a)"(x^2 - 2x - 2`
2x3 – 3x2
– +
–4x2 + 2x
–4x2 + 6x
+ –
–4x + a
–4x + 6
+ –
a – 6
But remainder is –2, then
a – 6 = –2
⇒ a = –2 + 6
⇒ a = 4
Hence 4 is to be added.
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