## RS Aggarwal Class 9 Solutions Chapter 2 Polynomials Ex 2D

These Solutions are part of RS Aggarwal Solutions Class 9. Here we have given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2D.

**Other Exercises**

- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2A
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2B
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2C
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2D
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2E
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2F
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2G
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2H
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2I
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2J
- RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2K

**Using factor theorem, show that :**

**Question 1.**

**(x – 2) is a factor of (x ^{3} – 8)**

**Solution:**

By factor theorem, x – 2 will be a factor of f(x) = x

^{3}– 8 if f(2) = 0

(∴ x-2 = 0=>x = 2)

Now f(2) = (2)

^{3}– 8 = 8- 8 = 0

Hence (x – 2) is a factor of f(x) Ans.

**Question 2.**

**(x – 3) is a factor of 2x ^{3} + 7x^{2} – 24x – 45**

**Solution:**

By factor theorem,

**Question 3.**

**(x – 1) is a factor of (2x ^{4} + 9x^{3} + 6x^{2}– 11x – 6)**

**Solution:**

By factor theorem,

(x – 1) is a factor of f(x)=(2x

^{4}+ 9x

^{3}+ 6x

^{2}– 11x – 6)

**Question 4.**

**(x + 2) is a factor of (x ^{2} – x^{2} – 12)**

**Solution:**

By factor theorem, (x + 2) will

a factor of f (x) = x

^{4}– x

^{4}+ 2

**Question 5.**

**(x + 5) is a factor of (2x ^{3} + 9x^{2} – 11x -30)**

**Solution:**

By factor theorem, (x + 5) will be a factor of f(x) = 2x

^{3}+ 9x

^{2}– 11x – 30 if f(-5) = 0

**Question 6.**

**(2x – 3) is a factor of (2x ^{4} + x^{3} – 8x^{2} – x + 6)**

**Solution:**

By factor theorem, (2x – 3) is a factor of f(x) = 2x

^{4}+ x

^{3}– 8x

^{2}– x + 6

**Question 7.**

**(x – √2) is a factor of (7x ^{2} – 4√2x – 6)**

**Solution:**

By factor theorem, (x – √2 ) will be a factor of f(x) = 7x

^{2}– 4√2x – 6

**Question 8.**

**(x + √2) is a factor of (2√2 x ^{3} + 5x +√2 )**

**Solution:**

By factor theorem, (x + √2) will be a factor of f(x) = 2√2 x

^{3}+ 5x + √2

**Question 9.**

**Find the value of k for which (x – 1) is a factor of (2x ^{3} + 9x^{2 }+ x + k).**

**Solution:**

Let f(x) = 2x

^{3}+ 9x

^{2}+ x + k and x – 1 is a factor of f(x)

**Question 10.**

**Find the value of a for which (x – 4) is a factor of (2x ^{3} – 3x^{2} – 18x + a).**

**Solution:**

Let f(x) = 2x

^{3}– 3x

^{2}– 18x + a and x – 4 is its factor

**Question 11.**

**Find the value of a for which the polynomial (x ^{4} – x^{3} – 11x^{2} – x + a) is divisible by (x + 3).**

**Solution:**

Let f(x) – x

^{4}– x

^{3}– 11x

^{2}– x + a

f(x) is divisible by (x + 3)

**Question 12.**

**For what value of a, the polynomial (2x ^{3} + ax^{2} + 11x + a + 3) is exactly divisible by (2x – 1) ?**

**Solution:**

Let f(x) = 2x

^{3}+ ax

^{2}+ 11x + a + 3

and (2x – 1) is its factor

Let 2x – 1 = 0 then 2x = 1

**Question 13.**

**Find the values of a and b so that the polynomial (x ^{3} – 10x^{2} + ax + b) is exactly divisible by (x – 1) as well as (x – 2).**

**Solution:**

Let f(x) = x

^{3}– 10x

^{2}+ ax + b and (x – 1) and (x – 2) are its factors

∴ x – 1 = 0 =>x=1

and x – 2 = 2 =>x=2

**Question 14.**

**Find the values of a and b so that the polynomial (x ^{4} + ax^{3} – 7x^{2} -8x + 6) is exactly divisible by (x + 2) as well as (x + 3).**

**Solution:**

Let f(x) = x

^{4}+ ax

^{3}– 7x

^{2}– 8x + b ,

and (x + 2) and (x + 3) are its factors

∴x + 2 = 0 => x = -2

and x + 3= 0 => x = -3

**Question 15.**

**Without actual division, show that (x ^{3} – 3x^{2} + 13x + 15) is exactly divisible by (x^{2} + 2x – 3).**

**Solution:**

Let f(x) = x

^{3}– 3x

^{2}– 13x + 15

Now x

^{2}+ 2x – 3 = x

^{2}+ 3x – x – 3

**Question 16.**

**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.**

**Solution:**

Let f(x) = x

^{3}+ ax

^{2}+ bx + 6 and (x – 2) is its factor

Let x – 2 = 0 then x = 2

Hope given RS Aggarwal Solutions Class 9 Chapter 2 Polynomials Ex 2D are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

muaz says

good but their is only one method to solve the problem

MUAZ says

Good.I am satisfy from your answer