- Constants and Variable
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- Polynomial expression
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- how to find the degree of a polynomial
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- Value of the polynomial
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- Zeros or roots of the polynomial
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- Adding Polynomials
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- subtracing Polynomials
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- Multiplying Polynomials
- |
- Dividing Polynomails
- |
- How to factor polynomials
- |
- Solved Examples Polynomials
- |

In this page we have ** NCERT book Solutions for Class 9th Maths:Polynomial** for
EXERCISE 1 . Hope you like them and do not forget to like , social share
and comment at the end of the page.

**Question 1:**

Which of the following expressions are polynomials in one variable and which are

not? State reasons for your answer.

4*x ^{2}*– 3

*y*^{2} + √2

3 √*t *+ *t*√ 2

*y *+ 2/y

*x*^{10} + *y*^{3} + *t*^{50}

**Solution:**

(i) 4*x ^{2}*– 3

Yes, this expression is a polynomial in one variable x.

(ii) *y*^{2} + √2

Yes, this expression is a polynomial in one variable y.

(iii) 3 √*t *+ *t*√ 2

No. It can be observed that the exponent of variable t in term 3 √*t* is 1/2, which is not a whole number. Therefore, this expression is not a polynomial.

(iv) y+2/y

No. It can be observed that the exponent of variable y in term 2/y is -1 which is not a whole number. Therefore, this expression is not a polynomial.

(v) *x*^{10} + *y*^{3} + *t*^{50}

No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable.

**Question 2**.

Write the coefficients of *x*2 in each of the following:

- 2 +
*x*^{2}+*x* - 2 –
*x*^{2}+*x*^{3} - (π/2)x
^{2}+ x - √ 2
*x*−1

**Solution:**

(i) 2+x^{2}+x

Coefficient of x^{2} is 1.

(ii) 2−x^{2}+x^{3}

Coefficient of x^{2} is -1.

(iii) (π/2)x^{2} + x

Coefficient of x^{2} is (π/2)

(iv) √ 2 *x *−1

There is no term consisting of x^{2}. Therefore, coefficient of x^{2} is 0.

**Question 3**

Give one example each of a binomial of degree 35, and of a monomial of degree 100.

**Solution:**

Degree of a polynomial is the highest power of variable in the polynomial.

Binomial has two terms in it. So binomial of degree 35 can be written as x^{35} + 1.

Monomial has only one term in it. So monomial of degree 100 can be written as x^{100}.

**Question 4**.

Write the degree of each of the following polynomials:

(i) 5*x*^{3} + 4*x*^{2} + 7*x *

(ii) 4 – *y*^{2}

(iii) 5*t *–√ 7

(iv) 3

**Solution:**

(i)** **This is a polynomial in variable x and the highest power of variable x is 3 Therefore, the degree of this polynomial is 3.

(ii)This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.

(iii) This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.

(iv)This is a constant polynomial. Degree of a constant polynomial is always 0.

**Question 5**.

Classify the following as linear, quadratic and cubic polynomials:

(i) *x*^{2} + *x*

(ii) *x *– *x*^{3}

(iii) *y *+ *y*^{2} + 4

(iv) 1 + *x*

(v) 3*t *

(vi) *r*^{2}

(vii) 7*x*^{3}

**Solution:**

(i) 2 + x^{2} + x is a quadratic polynomial as its degree is 2.

(ii) x – x^{3} is a cubic polynomial as its degree is 3.

(iii) y + y^{2} + 4 is a quadratic polynomial as its degree is 2.

(iv) 1 + x is a linear polynomial as its degree is 1.

(v) 3t is a linear polynomial as its degree is 1.

(vi) r^{2} is a quadratic polynomial as its degree is 2.

(vii) 7x^{3} is a cubic polynomial as its degree is 3.

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