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CBSE Class 9 Answered

  In the following problem use the factor theorem to find if g(x) is a factor of p(x): p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5
Asked by Topperlearning User | 14 Sep, 2017, 02:17: PM
answered-by-expert Expert Answer

straight g left parenthesis straight x right parenthesis space equals space straight x space plus space 5 space and space straight p left parenthesis straight x right parenthesis space equals space straight x cubed space plus space straight x squared space plus space 3 straight x space plus space 175 straight g left parenthesis straight x right parenthesis space will space be space straight a space factor space of space straight p left parenthesis straight x right parenthesis space if space straight p left parenthesis negative 5 right parenthesis space equals space 0 Thus comma space straight p left parenthesis negative 5 right parenthesis space equals space left parenthesis negative 5 right parenthesis cubed space plus space left parenthesis negative 5 right parenthesis squared space plus space 3 left parenthesis negative 5 right parenthesis space plus space 175 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 125 space plus space 25 space minus space 15 space plus space 175 space space space space space space space space space space space space space space space space space space space space space space equals space 60 space space space space space space space space space space space space space space space space space space space space space space not equal to space 0 Hence comma space straight g left parenthesis straight x right parenthesis space is space not space straight a space factor space of space straight p left parenthesis straight x right parenthesis.

Answered by | 14 Sep, 2017, 04:17: PM

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