Which of the following is correct? Every polynomial has finite number of multiples. LCM of two polynomials of degree 2 may be a constant. HCF of two polynomials may be a constant. A degree of HCF of two polynomials is always less than degree of LCM.
Answers
Answer: The answer is (c) H.C.F of two polynomials may be a constant.
Step-by-step explanation: We are familiar with the concept of polynomials. The degree of a polynomial is the highest power of the unknown variable in the polynomial.
First option is incorrect because a polynomial P(x) can have an infinite number of multiples. For example, if P(x)=x²-1, then we can have an infinite number of polynomials which are multiples of P(x), like 2P(x)=2x²-2, 3P(x)=3x²-3, etc.
Second option is also not correct because the L.C.M of two polynomials of degree 2 cannot be a constant. Here, the L.C.M will again be a polynomial of degree greater than or equal to 2. For example, if P(x)=x²-1 and Q(x)=x²-2x+1, then the L.C.M will be (x-1)²(x+1), which is not a constant.
The third option is correct, because the H.C.F of two polynomils may be a constant. For example, if P(x)=2x-2 and Q(x)=2x+2, then their H.C.F is 2, which is a constant.
The fourth option is also incorrect because sometimes the degree of the H.C.F and L.C.M of two polynomials may be same. For example, if P(x)=x²-1 and Q(x)=x²-1, the H.C.F=L.C.M=x²-1. So, degree of H.C.F=degree of L.C.M=2.
Thus, the correct option is (c).
I think option c friend.
I hope it is useful to u