NCERT solution Class 9 polynomials

NCERT Solutions

Class 9 Maths

Polynomials

NCERT Questions

Ex.2.1 Q.1
Ex.2.1 Q.2
Ex.2.1 Q.3
Ex.2.1 Q.4
Ex.2.1 Q.5
Ex.2.2 Q.1
Ex.2.2 Q.2
Ex.2.2 Q.3
Ex.2.2 Q.4
Ex.2.3 Q.1
Ex.2.3 Q.2
Ex.2.3 Q.3
Ex.2.4 Q.1
Ex.2.4 Q.2
Ex.2.4 Q.2
Ex.2.4 Q.3
Ex.2.4 Q.4
Ex.2.4 Q.5
Ex.2.5 Q.1
Ex.2.5 Q.2
Ex.2.5 Q.2
Ex.2.5 Q.4
Ex.2.5 Q.5
Ex.2.5 Q.6
Ex.2.5 Q.7
Ex.2.5 Q.8
Ex.2.5 Q.9
Ex.2.5 Q.10
Ex.2.5 Q.11
Ex.2.5 Q.12
Ex.2.5 Q.13
Ex.2.5 Q.14
Ex.2.5 Q.15
Ex.2.5 Q.16

Ex.2.3 Q.1

Find the remainder when x³ + 3x² + 3x + 1 is divided by

(1) x + 1

(2) x –

(3) x

(4) x + π

(5) 5 + 2x

Let p(x) = x³ + 3x² + 3x + 1

(1) put x + 1 = 0, we get

x = -1

Using remainder theorem, when p(x) = x³ + 3x² + 3x + 1 is divided by x + 1, remainder is given by p (-1).

Now, p (-1) = (-1)³ + 3 × (-1)² + 3 × (-1) + 1

= -1 + 3 – 3 + 1

= -4 + 4

= 0

Hence, the remainder is 0.

(2) put x – = 0, we get

x =

Using remainder theorem, when p(x) = x³ + 3x² + 3x + 1 is divided by x – , remainder is given

by p ( ).

Now, p ( ) = ( )³ + 3 × ( )² + 3 × ( ) + 1

= + 3 × + + 1

= + + + 1

= (1 × 1 + 3 × 2 + 3 × 4 + 1 × 8) ÷ 8

[LCM (8, 4, 2, 1) = 8]

= (1 + 6 + 12 + 8) ÷ 8

Hence, the remainder is .

(3) put x = 0

Using remainder theorem, when p(x) = x³ + 3x² + 3x + 1 is divided by x, remainder is given by p (0).

Now, p (-1) = (0)³ + 3 × (0)² + 3 × (0) + 1

= 0 + 0 + 0 + 1

= 1

Hence, the remainder is 1.

(4) put x + π = 0

Using remainder theorem, when p(x) = x³ + 3x² + 3x + 1 is divided by x + π, remainder is given

by p(-π).

Now, p(-π) = (-π)³ + 3 × (-π)² + 3 × (-π) + 1

= -π³ + 3 π³ - 3 π + 1

Hence, the remainder is -π³ + 3 π³ - 3 π + 1.

(5) put 5 + 2x = 0, we get

2x = -5

=> x = -

Using remainder theorem, when p(x) = x³ + 3x² + 3x + 1 is divided by 5 + 2x,

remainder is given by p (- ).

Now, p (- ) = (- )³ + 3 × (- )² + 3 × (- ) + 1

= - + 3 × - + 1

= - + - + 1

= (-1 × 125 + 75 × 2 - 15 × 4 + 1 × 8) ÷ 8

[LCM (8, 4, 2, 1) = 8]

= (-125 + 150 - 60 + 8) ÷ 8

= -

Hence, the remainder is .

Video solution:

Polynomials Class 9 Maths NCERT Chapter 2 NCERT Solutions

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NCERT solutions of Polynomials Class 9 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 9 Maths Polynomials NCERT solutions.