Find the values of a and b so that (x + 1) and (x − 1) are factors of x⁴ + ax³ − 3x² + 2x + b.

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Solution

Let be the given polynomial.

By factor theorem, and are the factors of f(x) if f(−1) and f(1) both are equal to zero.

Therefore,

and

Adding equation (i) and (ii), we get

Putting this value in equation (i), we get,

Hence, the value of a and b are – 2 and 2 respectively.

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