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a polynomial of degree if it is divided by the remainder is . if it is divided by , the remainder is . the polynomial is
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Q. a polynomial of degree if it is divided by the remainder is . if it is divided by , the remainder is . the polynomial is
- Polynomial Expression: Let's call the polynomial . Since is of degree , we can express it as .
- Division by First Polynomial: When is divided by , the remainder is . So, for some polynomial .
- Division by Second Polynomial: Similarly, when is divided by , the remainder is . So, for some polynomial .
- Equating Remainders: The remainders are equal when the divisors are equal, so we set and solve for . But this is incorrect, as the divisors are different and we cannot equate them. We should instead equate the remainders when the same value of is used.
