Question

1) Using division algorithm, find the dividend, if divisor, quotient and remainder
are (x - 3), (x - 2) and 2 respectively.​

Answer 1

Topic - Division Algorithm

• Theorem: Given integers a and b with b > 0, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b.

Now we solve the given problem:

• Divisor = x - 3
• Quotient = x - 2
• Remainder = 2

We know that,

Dividend = Divisor × Quotient + Remainder

Using this formula, we get

Dividend = (x - 3) (x - 2) + 2

= x² - 5x + 6 + 2

= x² - 5x + 8

∴ the required dividend = x² - 5x + 8.