Question

Can x2

– 1 be the quotient on division of x6 + 2x3

+ x – 1 by a polynomial

in x of degree 5?​

Answer 1

Answer:

No, because whenever we divide a polynomial x6+2x3+x-1 by a polynomial in x of degree 5, then we get quotient always as in linear form i.e., polynomial in x of degree 1. So, division algorithm is not satisfied. Hence, x2-1 is not a required quotient

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Answer 2

Answer:

No, x  

2

−1 cannot be the quotient on division of x  

6

−2x  

3

+x−1 by a  

polynomial in degree 5 because the degree of the product of the  

quotient and the divisor should be equal to the power of the dividend.

Here, the degree of the product of the quotient and the divisor is 7. But the degree of x  

6

−2x  

3

+x−1 is 6

Step-by-step explanation: