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

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 8B.

**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.**

**Using the Factor Theorem, show that:**

**(i) (x – 2) is a factor of x ^{3} – 2x^{2} – 9x +18. Hence, factorise the expression x^{3} – 2x^{2} – 9x + 18 completely.**

**(ii) (x + 5) is a factor of 2x**

^{3}+ 5x^{2}– 28x – 15. Hence, factorise the expression 2x^{3}+ 5x^{2}– 28x – 15 completely.**(iii) (3x + 2) is a factor of 3x**

^{3}+ 2x^{2}– 3x – 2. Hence, factorise the expression 3x^{3}+ 2x^{2}– 3x – 2. completely.**(iv) 2x + 7 is a factor of 2x**

^{3}+ 5x^{2}– 11x – 14. Hence, factorise the given expression completely.**Solution:**

**Question 2.**

**Using the Remainder Theorem, factorise each of the following completely:**

**(i) 3x ^{3} + 2x^{2} – 19x + 6**

**(ii) 2x**

^{3}+ x^{2}– 13x + 6**(iii) 3x**

^{3}+ 2x^{2}– 23x – 30**(iv) 4x**

^{3}+ 7x^{2}– 36x – 63**(v) x**

^{3}+ x^{2}– 4x – 4. (2004)**Solution:**

**Question 3.**

**Using the Remainder Theorem factorise the expression 3x ^{3} + 10x^{2} + x – 6. Hence, solve the equation. 3x^{3} + 10x^{2} + x – 6 = 0**

**Solution:**

**Question 4.**

**Factorise the expression f(x) = 2x ^{3} – 7x^{2} – 3x + 18. Hence, find all possible values of x for which f(x) = o.**

**Solution:**

**Question 5.**

**Given that x – 2 and x +1 are factors of f(x) = x ^{3} + 3x^{2} + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).**

**Solution:**

**Question 6.**

**The expression 4x ^{3} – bx^{2} + 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.**

**Solution:**

**Question 7.**

**If x + a is a common factor of expressions f(x) = x ^{2} + px + q and g (x) = x^{2} + mx + n show that a = \(\frac { n – q }{ m – p }\)**

**Solution:**

**Question 8.**

**The polynomials ax ^{3} + 3x^{2} – 3 and 2x^{3} – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.**

**Solution:**

**Question 9.**

**Find the value of ‘a’ if (x – a) is a factor of x ^{3} – ax^{2} + x + 2.**

**Solution:**

**Question 10.**

**Find the number that must be subtracted from the polynomial 3y ^{3} + y^{2} – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.**

**Solution:**

⇒ 9 – k = 0 ⇒ k = 9

Hence 9 should be subtracted.

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

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