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Factors of natural numbers

If f(x) = x3 ...

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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