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

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

If on dividing 2x³ + 6x² – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is

If x + 1 is a factor of 3x³ + kx² + 7x + 4, then the value of k is

Find the remainder when 2x³ – 3x² + 4x + 7 is divided by x – 2

Find the remainder when 2x³ – 3x² + 4x + 7 is divided by x + 3

Find the remainder when 2x³ – 3x² + 4x + 7 is divided by 2x + 1

When 2x³ – 9x² + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.

When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).

tan θ × `sqrt(1 - sin^2 θ)` is equal to:

Use graph paper for this question. Estimate the mode of the given distribution by plotting a histogram. [Take 2 cm = 10 marks along one axis and 2 cm = 5 students along the other axis]

(1 + sin A)(1 – sin A) is equal to ______.

Prove the following identity:

(sin²θ – 1)(tan²θ + 1) + 1 = 0

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