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Factor Theorem

Find the valu...

Question

Find the values of p and q so that x⁴ + px³ + 2x³ − 3x + q is divisible by (x² − 1).

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Solution

Let and be the given polynomials.

We have,

Here, are the factor of g(x).

If f(x) is divisible by and , then and are factor of f(x).

Therefore, f(1) and f(−1) both must be equal to zero.

Therefore,

and

Adding both the equations, we get,

Putting this value in (i)

Hence, the value of p and q are 3, −3 respectively.

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