# Introduction of Polynomials

**Covid-19 has led the world to go through a phenomenal transition .**

**E-learning is the future today.**

**Stay Home , Stay Safe and keep learning!!!**

Let x be a variable, n be a positive integer and a

_{0}, a

_{1},a

_{2}... ,a

_{n}be constants. Then,

f(x) = a

_{n}x

^{n}+ a

_{n-1}x

^{n-1}+ ... + a

_{1}x + a

_{0}is called a

**Poly-nomial**in variable x.

Here, a

_{n}x

^{n}, a

_{n-1}x

^{n-1}, ... , a

_{1}x, a

_{0}are known as

**terms**

and a

_{n}, a

_{n-1}, ..., a

_{1},a

_{0}are

**coefficients**.

**Examples**

1) p(x) = 3x -2 -----> polynomial in variable x.

2) q(y) = 3y

^{2}- 2y + 4 ------> is a poly-nomial in y.

3) f(u)= 1/2 u

^{3}- 3u

^{2}+ 2u - 4 ----> is a poly-nomial in variable u.

**Not a Poly-nomial :**If the exponent of any term is less than 1 or negative.

**Examples :**

1) 2x

^{2}- 3√x + 5

**Solution :**

It is not a poly-nomial because the exponent of one term is 1/2 which is less than 1.

2) 1/(x

^{2}- 2x + 5)

**Solution :**

It is not a poly-nomial because the exponent is negative.

3) 2x

^{3}- 3/x + 4

**Solution :**

As the exponent of 2nd term is -1 so it is not a poly-nomial.

_________________________________________________________________

**Practice**

Q.1 Write any poly-nomial in x with degree 3.

Q.2 P(x) = x

^{3}+ 2

^{3}- 4x + 8. Write the coefficient of x

^{2}.

Q.3 In P(x) = 5x

^{2}+ x

^{5}- 2x + 4 write the degree of poly-nomial.

Q.4 In P(x) = 1/2 x

^{3}- 7x

^{2}+ 8x, state the number of terms and write each terms.

**Polynomials**

• Degree of the Poly-nomial

• Zeros of Poly-nomial

• Remainder Theorem

• Find remainder by Synthetic Division

• Rational root test in Poly-nomial

• Solved Examples on Factorization

• Degree of the Poly-nomial

• Zeros of Poly-nomial

• Remainder Theorem

• Find remainder by Synthetic Division

• Rational root test in Poly-nomial

• Solved Examples on Factorization

**Home Page**

**Covid-19 has affected physical interactions between people.**

**Don't let it affect your learning.**