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Chapters
Chapter 2: Banking (Recurring Deposit Account)
Chapter 3: Shares and Dividend
Chapter 4: Linear Inequations (In one variable)
Chapter 5: Quadratic Equations
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
▶ Chapter 8: Remainder and Factor Theorems
Chapter 9: Matrices
Chapter 10: Arithmetic Progression
Chapter 11: Geometric Progression
Chapter 12: Reflection
Chapter 13: Section and Mid-Point Formula
Chapter 14: Equation of a Line
Chapter 15: Similarity (With Applications to Maps and Models)
Chapter 16: Loci (Locus and Its Constructions)
Chapter 17: Circles
Chapter 18: Tangents and Intersecting Chords
Chapter 19: Constructions (Circles)
Chapter 20: Cylinder, Cone and Sphere
Chapter 21: Trigonometrical Identities
Chapter 22: Height and Distances
Chapter 23: Graphical Representation
Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)
Chapter 25: Probability
Solutions for Chapter 8: Remainder and Factor Theorems
Below listed, you can find solutions for Chapter 8 of CISCE Selina for Concise Maths Class 10 ICSE.
Selina solutions for Concise Maths Class 10 ICSE Chapter 8 Remainder and Factor Theorems Exercise 8 (A) [Pages 108 - 109]
Find , in given case, the remainder when :
`x^4-3x^2+2x+1` is dividend by x-1
Find, in given case, the remainder when:
`x^3+3x^2-12x+4` is divided by x-2
Find , in given case the remainder when:
`x^4+1` is divided by x+1
show that
`x-2` is a factor of `5x^2+15x-50`
show that
`3x+2` is a factor of `3x^2-x-2`
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.
Find the value of k, if 3x – 4 is a factor of expression `3x^2` + 2x − k.
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1)
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1) x2 + nx – 18.
When `x^3 + 2x ^2– kx + 4 `is divided by x – 2, the remainder is k. Find the value of constant k.
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
If x3 + ax2 + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it with x – 2, the remainder is 10.
The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.
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
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
Selina solutions for Concise Maths Class 10 ICSE Chapter 8 Remainder and Factor Theorems Exercise 8 (B) [Pages 111 - 112]
Using the Factor Theorem, show that:
(x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
(x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
(3x + 2) is a factor of 3x3 + 2x2 – 3x – 2. Hence, factorise the expression 3x3 + 2x2 – 3x – 2 completely.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Using the Reminder Theorem, factorise of the following completely.
2x3 + x2 – 13x + 6
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Using the Remainder Theorem, factorise each of the following completely.
4x3 + 7x2 – 36x – 63
Using the Remainder Theorem, factorise each of the following completely
x3 + x2 – 4x – 4
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0.
Factorise the expression f (x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.
Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).
The expression 4x3 – bx2 + x – c leaves remainders 0 and 30 when divided by x + 1 and 2x – 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.
If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n;
show that : `a=(n-q)/(m-p)`
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.
Selina solutions for Concise Maths Class 10 ICSE Chapter 8 Remainder and Factor Theorems Exercise 8 (C) [Page 112]
Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.
Using Remainder Theorem, factorise:
x3 + 10x2 – 37x + 26 completely
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
If (x + 1) and (x – 2) are factors of x3 + (a + 1)x2 – (b – 2)x – 6, find the values of a and b. And then, factorise the given expression completely.
if x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
Factorise x3 + 6x2 + 11x + 6 completely using factor theorem.
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2
The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the values of p and q. Also, for these values of p and q factorize the given polynomial completely.
Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).
When the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
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’.
Using the Remainder Theorem, factorise each of the following completely.
2x3 + x2 – 13x + 6
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by x - 2, leaves a remainder 7
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has
2x + 1 as a factor?
Solutions for Chapter 8: Remainder and Factor Theorems
Selina solutions for Concise Maths Class 10 ICSE chapter 8 - Remainder and Factor Theorems
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Concepts covered in Concise Maths Class 10 ICSE chapter 8 Remainder and Factor Theorems are Factor Theorem, Remainder Theorem, Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.
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