(English Medium) ICSE Class 10 - CISCE Question Bank Solutions

Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x³ – 7x² + 3

Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 2x² – 5x + 1

Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where  f(x) = 3x³ + 7x² – 5x + 1

Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x² + 5x + 3

Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 3x³ – 7x² + 4x + 11

Find the remainder (without division) when 2x³ – 3x² + 7x – 8 is divided by x – 1 (2000)

Find the remainder (without division) on dividing 3x² + 5x – 9 by (3x + 2)

Using remainder theorem, find the value of a if the division of x³ + 5x² – ax + 6 by (x – 1) leaves the remainder 2a.

When divided by x – 3 the polynomials x³ – px² + x + 6 and 2x³ – x² – (p + 3)x – 6 leave the same remainder. Find the value of ‘p’.

Find ‘a’ if the two polynomials ax³ + 3x² – 9 and 2x³ + 4x + a, leaves the same remainder when divided by x + 3.

 What number must be subtracted from 2x² – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?

What number must be added to 2x³ – 7x² + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?

Use the Remainder Theorem to factorise the following expression:

2x³ + x² – 13x + 6

Using the Remainder Theorem, factorise completely the following polynomial: 

3x² + 2x² – 19x + 6

(x – 2) is a factor of the expression x³ + ax² + bx + 6. When this expression is divided by (x – 3), it leaves the remainder 3. Find the values of a and b. 

If (x – 2) is a factor of the expression 2x³ + ax² + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.

Given f(x) = ax² + bx + 2 and g(x) = bx² + ax + 1. If x – 2 is a factor of f(x) but leaves the remainder – 15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression. f(x) + g(x) + 4x² + 7x.

When x³ – 3x² + 5x – 7 is divided by x – 2,then the remainder is

When 2x³ – x² – 3x + 5 is divided by 2x + 1, then the remainder is

If on dividing 4x² – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is