## Selina Concise Mathematics Class 10 ICSE Solutions Chapter 8 Remainder and Factor Theorems Ex 8A

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 8 Remainder and Factor Theorems Ex 8A.

**Other Exercises**

- Selina Concise Mathematics Class 10 ICSE Solutions Chapter 8 Remainder and Factor Theorems Ex 8A
- Selina Concise Mathematics Class 10 ICSE Solutions Chapter 8 Remainder and Factor Theorems Ex 8B
- Selina Concise Mathematics Class 10 ICSE Solutions Chapter 8 Remainder and Factor Theorems Ex 8C

**Question 1.**

**Find in each case, the remainder when :**

**(i) x ^{4} – 3x^{2} + 2x + 1 is divided by x – 1.**

**(ii) x**

^{3}+ 3x^{2}– 12x + 4 is divided by x – 2.**(iii) x**

^{4}+ 1 is divided by x + 1.**(iv) 4x**

^{3}– 3x^{2}+ 2x – 4 is divided by 2x + 1.**(v) 4x**

^{3}+ 4x^{2}– 21x + 16 is divided by 2x – 3.**(vi) 2x**

^{3}+ 9x^{2}– x – 15 is divided by 2x + 3.**Solution:**

**Question 2.**

**Show that:**

**(i) x – 2 is a factor of 5x ^{2} + 15x – 50.**

**(ii) 3x + 2 is a factor of 3x**

^{2}– x – 2.**(iii) x + 1 is a factor of x**

^{3}+ 3x^{2}+ 3x + 1.**Solution:**

Polynomial Remainder Theorem Calculator is an online tool that displays the remainder of a polynomial easily.

**Question 3.**

**Use the Remainder Theorem to find which of the following is a factor of 2x ^{3} + 3x^{2} – 5x – 6.**

**(i) x + 1**

**(ii) 2x – 1**

**(iii) x + 2**

**(iv) 3x – 2**

**(v) 2x – 3.**

**Solution:**

(i) f(x) = 2×3 + 3×2 – 5x – 6

**Question 4.**

**(i) If 2x + 1 is a factor of 2x ^{2} + ax – 3, find the value of a.**

**(ii) Find the value of k, if 3x – 4 is a factor of expression 3x**

^{2}+ 2x – k.**Solution:**

**Question 5.**

**Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression, x ^{3} + ax^{2} + bx – 12.**

**Solution:**

(x + 3) is a factor of f(x)

f(-3) = 0

9a – 3b – 39 – 0

⇒ 3a – b – 13 = 0

⇒ 3a – b = 13

Adding (i) and (ii) we get:

5a = 15 ⇒ a = 3

Substituting the value of a in (i)

2(3) + b = 2

⇒ 6 + b = 2

⇒ b = 2 – 6 = – 4

Hence a = 3, b = – 4

**Question 6.**

**Find the value of k, if 2x + 1 is a factor of (3k + 2) x ^{3} + (k – 1).**

**Solution:**

**Question 7.**

**Find the value of a, if x – 2 is a factor of 2x ^{5} – 6x^{4} – 2ax^{3} + 6ax^{2} + 4ax + 8.**

**Solution:**

**Question 8.**

**Find the values of m and n so that x – 1 and x + 2 both are factors of x ^{3} + (3m + 1) x^{2} + nx – 18.**

**Solution:**

**Question 9.**

**When x ^{3} + 2x^{2} – kx + 4 is divided by x – 2, the remainder is k. Find the value of constants.**

**Solution:**

f(x) = x

^{3}+ 2x

^{2}– kx + 4

**Question 10.**

**Find the value of a, if the division of ax ^{3} + 9x^{2} + 4x – 10 by x + 3 leaves a remainder 5.**

**Solution:**

**Question 11.**

**If x ^{3} + ax^{2} + 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. [2005]**

**Solution:**

**Question 12.**

**The expression 2x ^{3} + ax^{2} + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.**

**Solution:**

**Question 13.**

**What number should be added to 3x ^{3} – 5x^{2} + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8 ?**

**Solution:**

**Question 14.**

**What number should be subtracted from x ^{3} + 3x^{2} – 8x + 14 so that on dividing it by x – 2, the remainder is 10.**

**Solution:**

**Question 15.**

**The polynomials 2x ^{3} – 7x^{2} + ax – 6 and x^{3} – 8x^{2} + (2a + 1) x – 16 leave the same remainder when divided by x – 2. Find the value of ‘a’.**

**Solution:**

**Question 16.**

**If (x – 2) is a factor of the expression 7x ^{3} + ax^{2} + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.**

**Solution:**

**Question 17.**

**Find ‘a’ if the two polynomials ax ^{3} + 3x^{2} – 9 and 2x^{3} + 4x + a, leave the same remainder when divided by x + 3. (2015)**

**Solution:**

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 8 Remainder and Factor Theorems Ex 8A are helpful to complete your math homework.

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