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CBSE Class 9 Answered

Prove that x + 3 is a multiple of q(x) = x3 + 6x2 + 11x + 6 using Remainder theorem.
Asked by Topperlearning User | 18 Sep, 2017, 09:35: AM
answered-by-expert Expert Answer

begin mathsize 12px style straight q left parenthesis straight x right parenthesis space equals space straight x cubed space plus space 6 straight x squared space plus space 11 straight x space plus space 6
straight q open parentheses negative 3 close parentheses space equals space open parentheses negative 3 close parentheses cubed space plus space 6 space cross times open parentheses negative 3 close parentheses squared space plus space 11 cross times open parentheses negative 3 close parentheses space plus space 6
straight q left parenthesis negative 3 right parenthesis space equals space minus 27 space plus space 54 space minus space 33 space plus 6
straight q left parenthesis negative 3 right parenthesis space equals space 0
Hence comma space left parenthesis straight x plus 3 right parenthesis space is space the space factor space of space straight q left parenthesis straight x right parenthesis. end style

Answered by | 18 Sep, 2017, 11:35: AM
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