Question

LCM OF 2(X+1)(X^2-4), GCD IS (X+1) ,p(x) = (x+1) (x-2) find q(x)​

Answer 1

Step-by-step explanation:

We know that if p(x) and q(x) are two polynomials, then p(x)×q(x)= {GCD of p(x) and q(x)}× {LCM of p(x) and q(x)}.

Now, it is given that one of the polynomial is p(x)=(x+1)(x−2), the LCM is 2(x+1)(x

2

−4) and the GCD is x+1, therefore, we have:

((x+1)(x−2))(q(x))=(x+1)×2(x+1)(x

2

−4)

⇒((x+1)(x−2))(q(x))=2(x+1)

2

×(x

2

−2

2

)

⇒((x+1)(x−2))(q(x))=2(x+1)

2

×(x+2)(x−2)(∵(a+b)

2

=a

2

+b

2

+2ab)

⇒((x+1)(x−2))(q(x))=2(x+1)

2

(x+2)(x−2)

⇒q(x)=

(x+1)(x−2)

2(x+1)

2

(x+2)(x−2)

⇒q(x)=2(x+1)(x+2)

Hence, the other polynomial q(x) is 2(x+1)(x+2).