# RS Aggarwal Solutions Class 9 Polynomials

Question 1:

Which of the following expressions are polynomials?

(i) x5 -2x3 + x+7

It is a polynomial, Degree = 5.

(ii) y3 3y$\sqrt{3}y$

It is polynomial, Degree = 3.

(iii) t225t+2$\frac{2}{5}t+\sqrt{2}$

It is polynomial, Degree = 2.

(iv) 5z6$5\sqrt{z}-6$

It is not a polynomial.

(v) x1x$x-\frac{1}{x}$

It is not a polynomial.

(vi) x1081$x^{108}-1$

It is polynomial, Degree = 108.

(vii) x327$\sqrt[3]{x}-27$

It is not a polynomial.

(viii) 12x22x+2$\frac{1}{\sqrt{2}}x^{2}-\sqrt{2}x+2$

It is a polynomial, Degree = 2.

(ix) x2+2x1+3$x^{-2}+2x^{-1}+3$

It is not a polynomial.

(x) 1

It is a polynomial, Degree = 0.

(xi) –35$\frac{3}{5}$

It is a polynomial, Degree = 0.

(xii) 23y28$\sqrt[3]{2}y^{2}-8$

It is a polynomial, Degree = 2.

Question 2:

Write the degree of each of the following polynomials:

The degree of a polynomial in one variable is the highest power of the variable.

(i)2x-5$\sqrt{5}$

Degree of 2x – 5$\sqrt{5}$ is 1.

(ii) 3 – x + x2-6x3

Degree of 3 – x + x2– 6x3 is 3.

(iii)9

Degree of 9 is 0.

(iv) 8x4-36x+5x7

Degree of 8x4 – 36x + 5x7 is 7.

(v)x9-x5+3x10+8

Degree of x9 – x5 3x10 + 8 is 10.

(vi) 2-3x2

Degree of 2 – 3x2 is 2.

Question 3:

Write :

(i) Coefficient of x3 in 2x + x2 – 5x3+ x4

-5

(ii) Coefficient of x in 3$\sqrt{3}$ – 22x$\sqrt{2x}$ + 4x2

— 22$\sqrt{2}$

(iii) Coefficient of x2 in ÷3$\prod \div 3$ x2 + 7x-3

÷3$\prod \div 3$

(iv)   Coefficient of x2 in 3x – 5

0.

Question 4:

(i) Give an example of a binomial of degree 27.

x27 — 36

(ii) Give an example of a monomial of degree 16.

y116

(iii) Give an example of a trinomial of degree 3.

5x3 — 8x + 7

Question 5:

Classify the following as linear, quadratic and cubic polynomials :

(i)               2x2 + 4x

It is a quadratic polynomial.

(ii)         x – x3

It is a cubic polynomial.

(iii)       2 – y – y2

It is a quadratic polynomial.

(iv)   -7 + z

It is a linear polynomial.

(v)     5t

It is a linear polynomial.

(vi)    p3

It is a cubic polynomial.

Question 6:

If p(x) = 5 – 4x + 2x2, find

(i) p(0)

= 5 – 4(0) + 2(0)2

= 5

(ii) p(3)

= 5 – 4(3) + 2(3)2

= 5 – 12 + 18

= 23 – 12

= 11

(iii) p(-2)

= 5 – 4(-2) + 2(-2)2

= 5 + 8 + 8

= 21

Question 7:

If P(Y) = 4 + 3Y – Y2+ 5y3 , find

(i) p(0)

= 4 + 3(0) – 02 + 5(0)3

= 4 + 0 – 0 + 0

= 4

(ii) p(2)

= 4 + 3(2) – 22 + 5(2)3

= 4 + 6 – 4 + 40

= 10 – 4 + 40

= 46

(III) p(-1)

= 4 + 3(-1) – (-1)2 + 5(-1)3

= 4 – 3 – 1 – 5

= -5

Question 8:

If f(t) = 4t2 – 3t + 6, find

(i) f(0)

= 4(0)2 – 3(0) + 6

= 0 – 0 + 6

= 6

(ii) f(4)

= 4(4)2 – 3(4) + 6

= 64 – 12 + 6

= 58

(iii) f(-5)

= 4(-5)2 – 3(-5) + 6

= 100 + 15 + 6

= 121

#### Practise This Question

In order to attain octet configuration, the atoms share, lose or gain electrons, then its atomic mass