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Remainder Theorem

If the polyno...

Question

If the polynomials 2x³ + ax² + 3x − 5 and x³ + x² − 4x +a leave the same remainder when divided by x −2, find the value of a.

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Solution

Let us denote the given polynomials as

Now, we will find the remaindersandwhenandrespectively are divided by.

By the remainder theorem, whenis divided bythe remainder is

By the remainder theorem, whenis divided bythe remainder is

By the given condition, the two remainders are same. Then we have,

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