(English Medium) ICSE Class 10 - CISCE Important Questions for Mathematics

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

Using the Remainder and Factor Theorem, factorise the following polynomial:

`x^3 + 10x^2 - 37x + 26`

A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.

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.

Using the Remainder Theorem, factorise the following completely:

3x³ + 2x² – 19x + 6

Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.

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’.

Use the Remainder Theorem to factorise the following expression:]

`2x^3 + x^2 - 13x + 6`

Using the factor theorem, show that (x - 2) is a factor of `x^3 + x^2 -4x -4 .`

Hence factorise the polynomial completely.

Using the remainder theorem, find the remainders obtained when x³ + (kx + 8 )x + k is divided by x + 1 and x − 2. 

Hence, find k if the sum of the two remainders is 1.

If x – 2 is a factor of x³ – kx – 12, then the value of k is ______.

Find the value of 'a' if x – a is a factor of the polynomial 3x³ + x² – ax – 81.

Factorize completely using factor theorem:

2x³ – x² – 13x – 6

What must be subtracted from the polynomial x³ + x² – 2x + 1, so that the result is exactly divisible by (x – 3)?

The polynomial 3x³ + 8x² – 15x + k has (x – 1) as a factor. Find the value of k. Hence factorize the resulting polynomial completely.

A polynomial in ‘x’ is divided by (x – a) and for (x – a) to be a factor of this polynomial, the remainder should be ______.

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

For what value of n, the n^th terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?

In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms. 

The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.