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.1

Determine which of the following polynomials has (x + 1) a factor:

(1) x³ + x² + x + 1

(2) x⁴ + x³ + x² + x + 1

(3) x⁴ + 3x³ + 3x² + x + 1

(4) x³ – x² – (2 + √2) x + √2

(1) For x + 1 = 0, we have x = –1

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

= –1 + 1 – 1 + 1

= 0

i.e., when p(x) is divided by (x + 1), then the remainder is zero.

So, (x + 1) is a factor of x³ + x² + x + 1.

(2) For x + 1 = 0, we have x = –1.

Now, p (–1) = (–1)⁴ + (–1)³ + (–1)² + (–1) + 1

= 1 –1 + 1 – 1 + 1

= 1

i.e., when p(x) is divided by (x + 1), then the remainder is zero.

Since p(x) is not divisible by x + 1

Hence, (x + 1) is not a factor of x⁴ + x³ + x² + x + 1.

(3) For x + 1 = 0, we have x = –1.

Now, p (–1) = (–1)⁴ + 3(–1)³ + 3(–1)² + (-1) + 1

= 1 – 3 + 3 – 1 + 1

= 1

i.e., when p(x) is divided by (x + 1), then the remainder is zero.

Since p(x) is not divisible by x + 1.

Hence, (x + 1) is not a factor of x⁴ + 3x³ + 3x² + x + 1.

(4) x³ – x² – (2 + √2) x + √2

For x + 1 = 0, we have x = –1.

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

= –1 - 1 + (2 + √2) + √2

= 2√2

i.e., when p(x) is divided by (x + 1), then the remainder is zero.

Since p(x) is not divisible by x + 1

So, (x + 1) is not a factor of x³ – x² – (2 + √2) x + √2.

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.