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Division Algorithm for a Polynomial

If fx=x3+x2-a...

Question

If f(x) = x³ + x² − ax + b is divisible by x² − x write the value of a and b.

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Solution

We are given is exactly divisible by then the remainder should be zero

Therefore Quotient and

Remainder

Now, Remainder

Equating coefficient of x, we get

.

Equating constant term

Hence, the value of a and b are

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