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Question
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
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Solution
Let the required number be k.
Let f(x) = 3x3 – 8x2 + 4x – 3 – k
According to the given information,
f(–2) = 0
3(–2)3 – 8(–2)2 + 4(–2) – 3 – k = 0
–24 – 32 – 8 – 3 – k = 0
–67 – k = 0
k = –67
Thus, the required number is –67.
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