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.2.4 Q.2

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:

(1) p(x) = 2x³ + x² – 2x – 1, g(x) = x + 1

(2) p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

(3) p(x) = x³ - 4x² + x + 6, g(x) = x - 3

(1) Given, p(x) = 2x³ + x² – 2x – 1, g(x) = x + 1

Put x + 1 = 0, we get x = -1

Using remainder theorem, when p(x) = 2x³ + x² – 2x – 1 is divided by g(x) = x + 1, remainder is given by p (-1).

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

= -2 + 1 + 2 – 1

= -3 + 3

= 0

Since remainder p (-1) = 0, hence g(x) is a factor of p(x).

(2) Given, p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

Put x + 2 = 0, we get x = -2

Using remainder theorem, when p(x) = x³ + 3x² + 3x + 1 is divided by g(x) = x + 2, remainder is given by p (-2).

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

= -8 + 3 × 4 – 3 × 2 + 1

= -8 + 12 – 6 + 1

= -14 + 13

= -1

Since remainder p (-2) ≠ 0, hence g(x) is not a factor of p(x).

(3) Given, p(x) = x³ - 4x² + x + 6, g(x) = x – 3

Put x - 3 = 0, we get x = 3

Using remainder theorem, when p(x) = x³ - 4x² + x + 6 is divided by g(x) = x - 3, remainder is given by p (3).

Now, p (3) = 3³ - 4 × 3² + 3 + 6

= 27 - 4 × 9 + 3 + 6

= 27 - 36 + 3 + 6

= 36 - 36

= 0

Since remainder p (3) = 0, hence g(x) is a factor of p(x).

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.