Question

the LCM and HCF of two polynomials p(x) and q(x) are 2(x^4-1) and (x+1) (x^2+1) respectively if p(x)=x^3+x^2+x+1 find q(x)


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Answer 1

Answer:

Given,

LCM of p(x) and q(x)= 2(x⁴-1).

HCF of p(x) and q(x)= (x+1)(x²+1).

Value of p(x)= x³+x²+x+1.

To Find,

Value of q(x).

Solution,

We can simply solve the problem by diving the LCM of p(x) and q(x) by p(x).

Then we will get a factor of q(x) that must be multiplied to HCF to get q(x).

LCM= lowest common multiple.

HCF= Highest common factor.

Diving LCM of p(x) and q(x) by p(x), we get = (2x-2).

So, (2x-2) must be multiplied by HCF to get q(x).

Multiplying, we get= (x+1)(x²+1)(2x-2).

Hence, the value of q(x) is (x+1)(x²+1)(2x-2).