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

The bisectors of ∠B and ∠C of a quadrilateral ABCD intersect in P. Show that P is equidistant from the opposite sides AB and CD.

By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x² + 5x – 3.

Show that (x – 2) is a factor of 3x² – x – 10 Hence factorise 3x² – x – 10.

Show that (x – 1) is a factor of x³ – 5x² – x + 5 Hence factorise x³ – 5x² – x + 5.

Show that (x – 3) is a factor of x³ – 7x² + 15x – 9. Hence factorise x³ – 7x² + 15 x – 9

Show that (2x + 1) is a factor of 4x³ + 12x² + 11 x + 3 .Hence factorise 4x³ + 12x² + 11x + 3.

Show that 2x + 7 is a factor of 2x³ + 5x² – 11x – 14. Hence factorise the given expression completely, using the factor theorem. 

Use factor theorem to factorise the following polynominals completely.

x³ + 2x² – 5x – 6

Use factor theorem to factorise the following polynominals completely. x³ – 13x – 12.

Using the Remainder and Factor Theorem, factorise the following polynomial: x³ + 10x² – 37x + 26.

If (2x + 1) is a factor of 6x³ + 5x² + ax – 2 find the value of a.

If (3x – 2) is a factor of 3x³ – kx² + 21x – 10, find the value of k.

Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation, (K + 2)x² – Kx + 6 = 0. Also, find the other root of the equation.

What number should be subtracted from 2x³ – 5x² + 5x so that the resulting polynomial has 2x – 3 as a factor?

Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x³ + ax² + bx – 12.

If (x + 2) and (x – 3) are factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

If ax³ + 3x² + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.

If (2x – 3) is a factor of 6x² + x + a, find the value of a. With this value of a, factorise the given expression.

Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.

How many terms of the A.P. 27, 24, 21, …, should be taken so that their sum is zero?