In the following problem, use the factor theorem to find if g(x) = x - 2 is a factor of p(x) = x3 - 3x2 + 4x - 4.

CBSE Class 9 Answered

In the following problem, use the factor theorem to find if g(x) = x - 2 is a factor of p(x) = x³ - 3x² + 4x - 4.

Asked by Topperlearning User | 14 Sep, 2017, 01:43: PM

Expert Answer

$straight g left parenthesis straight x right parenthesis space equals space straight x space minus space 2 space and space straight p left parenthesis straight x right parenthesis space equals space straight x cubed space minus space 3 straight x squared space plus space 4 straight x space minus space 4 straight g left parenthesis straight x right parenthesis space will space be space straight a space factor space of space straight p left parenthesis straight x right parenthesis space if space straight p left parenthesis 2 right parenthesis space equals space 0 Thus comma space straight p left parenthesis 2 right parenthesis space equals space left parenthesis 2 right parenthesis cubed space minus space 3 left parenthesis 2 right parenthesis squared space plus space 4 left parenthesis 2 right parenthesis space minus space 4 space space space space space space space space space space space space space space space space space space space equals space 8 space minus space 12 space plus space 8 space minus space 4 space space space space space space space space space space space space space space space space space space space equals space 0 Hence comma space straight g left parenthesis straight x right parenthesis space is space straight a space factor space of space straight p left parenthesis straight x right parenthesis.$

Answered by | 14 Sep, 2017, 03:43: PM