## 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.**

**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.**

**Solution:**

By factor theorem,

**Question 3.**

**Solution:**

By factor theorem,

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

**Question 4.**

**Solution:**

By factor theorem, (x + 2) will

a factor of f (x) = x^{4} – x^{4} + 2

**Question 5.**

**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.**

**Solution:**

By factor theorem, (2x – 3) is a factor of f(x) = 2x^{4} + x^{3} – 8x^{2} – x + 6

**Question 7.**

**Solution:**

By factor theorem, (x – √2 ) will be a factor of f(x) = 7x^{2} – 4√2x – 6

**Question 8.**

**Solution:**

By factor theorem, (x + √2) will be a factor of f(x) = 2√2 x^{3} + 5x + √2

**Question 9.**

**Solution:**

Let f(x) = 2x^{3} + 9x^{2} + x + k and x – 1 is a factor of f(x)

**Question 10.**

**Solution:**

Let f(x) = 2x^{3} – 3x^{2} – 18x + a and x – 4 is its factor

**Question 11.**

**Solution:**

Let f(x) – x^{4} – x^{3} – 11x^{2} – x + a

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

**Question 12.**

**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.**

**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.**

**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.**

**Solution:**

Let f(x) = x^{3} – 3x^{2} – 13x + 15

Now x^{2} + 2x – 3 = x^{2} + 3x – x – 3

**Question 16.**

**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.

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