Given p(x)=x^3-4x^2+x+6 and g(x)=x-3 verify whether g(x) is a factor of p(x) or not and state the reason.

1 thought on “Given p(x)=x^3-4x^2+x+6 and g(x)=x-3 verify whether g(x) is a factor of p(x) or not and state the reason.”

1. Step-by-step explanation:

   Given :–

   p(x)=x^3-4x^2+x+6

   and g(x)=x-3

   To find :–

   Verify whether g(x) is a factor of p(x) or not? and state the reason.

   Solution:–

   Given Polynomial P(x) = x^3-4x^2+x+6

   Given divisor g(x) = x-3

   If g(x) = x-3 is a factor of P(x) then by factor theorem , P(3) = 0

   Factor Theorem :

   Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice-versa.

   P(3) = (3)^3-4(3)^2+3+6

   => 27-4(9)+3+6

   => 27 – 36+9

   =>36-36

   => 0

   P(3) = 0

   Answer:–

   g(x) = x-3 is a factor of P(x) = x^3-4x^2+x+6 .

   Reason :-

   P(3) = 0 i.e.g(x) satisfies the given Polynomial P(x)

   Used formulae:–

   Factor Theorem :

   Let P(x) be a polynomial of the degree greater than or equal to 1 and x-a is another linear polynomial if x-a is a factor of P (x) then P(a) = 0 vice-versa.

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