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CBSE Class 9 Answered

Using Remainder Theorem, obtain the remainder when(i) p(x) = 2x4 - 3x3 + x2 - x + 5 is divided by (x - 2)(ii) q(x) = 4x3 - 12x2 + 14x - 3 is divided by (2x - 1)
Asked by Topperlearning User | 18 Sep, 2017, 09:25: AM
answered-by-expert Expert Answer

left parenthesis straight i right parenthesis space space space straight p left parenthesis straight x right parenthesis space space equals space 2 straight x to the power of 4 space minus space 3 straight x cubed space plus space straight x squared space minus space straight x space plus space 5
space space space space space space straight x space minus space 2 space equals space 0 space rightwards double arrow space straight x space equals space 2
space space space space space space Remainder space equals straight p left parenthesis 2 right parenthesis space equals space 2 left parenthesis 2 right parenthesis to the power of 4 space minus space 3 left parenthesis 2 right parenthesis cubed space plus space left parenthesis 2 right parenthesis squared space minus space 2 space plus space 5 space equals space 32 space minus space 24 space plus space 4 space plus space 3 space equals space 15 space space

left parenthesis ii right parenthesis space space straight q left parenthesis straight x right parenthesis space space equals space 4 straight x cubed space minus space 12 straight x squared space plus space 14 straight x space minus space 3
space space space space space space 2 straight x space minus space 1 space equals space 0 space rightwards double arrow space straight x space equals space 1 half
space space space space space space Remainder space equals straight q open parentheses 1 half close parentheses space equals space 4 open parentheses 1 half close parentheses cubed space minus space 12 open parentheses 1 half close parentheses squared space plus space 14 open parentheses 1 half close parentheses space minus space 3 space equals space 1 half space minus space 3 space plus space 7 space minus space 3 space equals space 3 over 2

Answered by | 18 Sep, 2017, 11:25: AM
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