Exercise 2.4

NCERT solutions for Class 9 Maths Polynomials 

 NCERT Solutions for Class 9 Maths Polynomials

1. Determine which of the following polynomials hasa factor:

(i)

(ii)

(iii)

(iv)

Ans. (i)

While applying the factor theorem, we get

=-1+1-1+1

=0

We conclude that on dividing the polynomialby, we get the remainder as0.

Therefore, we conclude thatis a factor of.

(ii)

While applying the factor theorem, we get

=1-1+1-1+1

=1

We conclude that on dividing the polynomialby, we will get the remainder as1, which is not 0.

Therefore, we conclude thatis not a factor of.

(iii)

While applying the factor theorem, we get

=1-3+3-1+1

=1

We conclude that on dividing the polynomialby, we will get the remainder as 1, which is not 0.

Therefore, we conclude thatis not a factor of.

(iv)

While applying the factor theorem, we get

We conclude that on dividing the polynomialby, we will get the remainder as, which is not 0.

Therefore, we conclude thatis not a factor of.

NCERT Solutions for Class 9 Maths Exercise 2.4

2. Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the

following cases:

(i)

(ii)

(iii)

Ans. (i)

We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(-1)=0.

=2+1-1-2

=0

Therefore, we conclude that the g(x) is a factor of p(x).

(ii)

We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(-2)=0.

=-8+12-6+1

=-1

Therefore, we conclude that the g(x) is not a factor of p(x).

(iii)

We know that according to the factor theorem,

We can conclude that g(x) is a factor of p(x), if p(3)=0.

=27-36+3+6

=0

Therefore, we conclude that the g(x) is a factor of p(x).

NCERT Solutions for Class 9 Maths Exercise 2.4

3. Find the value of k, if x – 1 is a factor of p(x) in each of the following cases:

(i)

(ii)

(iii)

(iv)

Ans. (i)

We know that according to the factor theorem

.

We conclude that ifis a factor of, then.

or

Therefore, we can conclude that the value of k is.

(ii)

We know that according to the factor theorem

.

We conclude that ifis a factor of, then.

or

Therefore, we can conclude that the value of k is.

(iii)

We know that according to the factor theorem

.

We conclude that ifis a factor of, then.

or

Therefore, we can conclude that the value of k is.

(iv)

We know that according to the factor theorem

is a factor of p(x)

We conclude that ifis a factor of, then.

or

Therefore, we can conclude that the value of k is.

NCERT Solutions for Class 9 Maths Exercise 2.4

4. Factorize:

(i)

(ii)

(iii)

(iv)

Ans. (i)

Therefore, we conclude that on factorizing the polynomial, we get.

(ii)

Therefore, we conclude that on factorizing the polynomial, we get.

(iii)

Therefore, we conclude that on factorizing the polynomial, we get.

(iv)

Therefore, we conclude that on factorizing the polynomial, we get.

NCERT Solutions for Class 9 Maths Exercise 2.4

5. Factorize:

(i)

(ii)

(iii)

(iv)

Ans. (i)

We need to consider the factors of 2, which are.

Let us substitute 1 in the polynomial, to get

=1-1-2+2=0

Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get .

(ii)

We need to consider the factors of, which are.

Let us substitute 1 in the polynomial, to get

Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get .

(iii)

We need to consider the factors of 20, which are.

Let us substitutein the polynomial, to get

=-1+13-32+20=-20+20=0

Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get.

(iv)

We need to consider the factors of, which are.

Let us substitute 1 in the polynomial, to get

=2+1-2-1=3-3=0

Thus, according to factor theorem, we can conclude thatis a factor of the polynomial.

Let us divide the polynomialby, to get

Therefore, we can conclude that on factorizing the polynomial, we get.