CBSE Class 9 Answered

Find remainder using Remainder theorem:(i) r(t) = t³ + 6t² + 2t - 2 is divided by (3t + 1)(ii) g(y) = y³ - 6y² + 2y - 4 is divided by (1 - 3y)

Asked by Topperlearning User | 18 Sep, 2017, 09:30: AM

Expert Answer

$left parenthesis straight i right parenthesis space space space When space straight r left parenthesis straight t right parenthesis space equals space straight t cubed space plus space 6 straight t squared space plus space 2 straight t space minus space 2 space is space divided space by space left parenthesis 3 straight t space plus space 1 right parenthesis comma space space space space space space space Remainder space equals space straight r open parentheses negative 1 third close parentheses space equals space open parentheses negative 1 third close parentheses cubed space plus space 6 open parentheses negative 1 third close parentheses squared space plus space 2 open parentheses negative 1 third close parentheses space minus space 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space minus 1 over 27 space plus space 2 over 3 space minus space 2 over 3 space minus space 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator negative 1 space minus space 54 over denominator 27 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative 55 over 27 left parenthesis ii right parenthesis space space space When space straight g left parenthesis straight y right parenthesis space equals space straight y cubed space minus space 6 straight y squared space plus space 2 straight y space minus space 4 space is space divided space by space left parenthesis 1 space minus space 3 straight y right parenthesis comma space space space space space space space Remainder space equals space straight g open parentheses 1 third close parentheses space equals space open parentheses 1 third close parentheses cubed space minus space 6 open parentheses 1 third close parentheses squared space plus space 2 open parentheses 1 third close parentheses space minus space 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1 over 27 space minus space 2 over 3 space plus space 2 over 3 space minus space 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 1 space minus space 108 over denominator 27 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals negative 107 over 27$