Question

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Answer 1

Answer:

2x - 3

Step-by-step explanation:

(1)

When polynomial p(x) is divided by (x - 2), the remainder is 1.

Thus, p(2) = 1

(2)

When polynomial p(x) is divided by (x - 3), the remainder is 3.

Thus, p(3) = 3

Given that remainder when p(x) is divided by (x - 2)(x - 3).

When the polynomial is divided by (x - 2)(x - 3), the remainder R will be of the form Ax + B.

Hence,

P(x) = Q * D + Ax + B

So,

P(2) = Q * 0 + 2A + B

=> 1 = 2A + B    ------ (1)

P(3) = Q * 0 + 3A + B

=> 3 = 3A + B    ------ (2)

On solving (1) & (2), we get

2A + B = 1

3A + B = 3

-------------------

A = 2

Place the value of A = 2 in (1), we get

2A + B = 1

=> 4 + B = 1

=> B = -3

Therefore,

Remainder = 2x - 3.

Hope it helps!