# Introduction of Polynomials

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Polynomials are algebraic expressions that include real numbers and variables. Division and square roots cannot be involved in the variables. The variables can only include addition, subtraction and multiplication.

Let x be a variable, n be a positive integer and a0, a1,a2... ,an be constants. Then,
f(x) = anx n + an-1xn-1+ ... + a1x + a0 is called a Poly-nomial in variable x.

Here, anx n, an-1xn-1, ... , a1x, a0 are known as terms
and an, an-1, ..., a1,a0 are coefficients.

Examples

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

2) q(y) = 3y2 - 2y + 4 ------> is a poly-nomial in y.

3) f(u)= 1/2 u3 - 3u2 + 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) 2x2 - 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/(x2 - 2x + 5)

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

3) 2x3 - 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) = x3 + 23 - 4x + 8. Write the coefficient of x2.
Q.3 In P(x) = 5x2 + x5 - 2x + 4 write the degree of poly-nomial.
Q.4 In P(x) = 1/2 x3 - 7x2 + 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