Question

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.

Answer 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.