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**Q.1. Find the remainder when x ^{3}+3x^{2}+3x+1 is divided by**

x+1= 0

⇒ x = −1

∴ Remainder:

p(−1) = (−1)

= −1+3−3+1

= 0

**(ii) x−1/2****Solution:**

x-1/2 = 0

⇒ x = 1/2

∴ Remainder:

p(1/2) = (1/2)^{3}+3(1/2)^{2}+3(1/2)+1

= (1/8)+(3/4)+(3/2)+1

= 27/8

**(iii) x****Solution:**

x = 0

∴ Remainder:

p(0) = (0)^{3}+3(0)^{2}+3(0)+1

= 1

**(iv) x+π****Solution:**

x+π = 0

⇒ x = −π

∴ Remainder:

p(0) = (−π)^{3} +3(−π)^{2}+3(−π)+1

= −π^{3}+3π^{2}−3π+1

**(v) 5+2x****Solution:**

5+2x=0

⇒ 2x = −5

⇒ x = -5/2

∴ Remainder:

(-5/2)^{3}+3(-5/2)^{2}+3(-5/2)+1 = (-125/8)+(75/4)-(15/2)+1

= -27/8

**Q.2. Find the remainder when x ^{3}−ax^{2}+6x−a is divided by x-a.**

Let p(x) = x

x−a = 0

∴ x = a**Remainder:**

p(a) = (a)^{3}−a(a^{2})+6(a)−a = a^{3}−a^{3}+6a−a = 5a

**Q.3. Check whether 7+3x is a factor of 3x3+7x.****Solution:**

7+3x = 0

⇒ 3x = −7

⇒ x = -7/3

∴ Remainder:

3(-7/3)^{3}+7(-7/3) = -(343/9)+(-49/3)

= (-343-(49)3)/9

= (-343-147)/9

= -490/9 ≠ 0

∴ 7+3x is not a factor of 3x3+7x

**Check out the NCERT Solutions of all the exercises of Polynomials: **

Exercise 2.1. NCERT Solutions: Polynomials

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