ML Aggarwal solutions for Understanding ICSE Mathematics [English] Class 10 chapter 6 - Factorization [Latest edition]

Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x² – 1x + 4

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 k if on dividing 2x³ + 3x² – kx + 5 by x – 2, leaves a remainder 7.

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

 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?

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.

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.

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

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.

If (x – 2) is a factor of 2x³ – x² + px – 2, then
(i) find the value of p.
(ii) with this value of p, factorise the above expression completely

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.

(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.

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.

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.

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

When 3x² – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x² – 5x + p – 3.

Prove that (5x + 4) is a factor of 5x³ + 4x² – 5x – 4. Hence factorize the given polynomial completely.

Use factor theorem to factorise the following polynomials completely: 4x³ + 4x² – 9x – 9

Use factor theorem to factorise the following polynomials completely: x³ – 19x – 30

If x³ – 2x² + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorize the given polynomial completely.

If (x + 3) and (x – 4) are factors of x³ + ax² – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.

f 2x³ + ax² – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorize the given expression.

If (2x + 1) is a factor of both the expressions 2x² – 5x + p and 2x² + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.

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).