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What Should Be Subtracted from 3x3 – 8x2 + 4x – 3, So that the Resulting Expression Has X + 2 as a Factor? - ICSE Class 10 - Mathematics

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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? 

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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Solution What Should Be Subtracted from 3x3 – 8x2 + 4x – 3, So that the Resulting Expression Has X + 2 as a Factor? Concept: Factor Theorem.
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