- Introduction
- Geometric Meaning of the Zero's of the polynomial
- Relation between coefficient and zero's of the Polynomial
- Formation of polynomial when the zeros are given
- Division algorithm for Polynomial

- We have studied polynomial expression in one variable and their degrees in the previous classes.
- Now we know that the highest power of x in p(x) is called the degree of the polynomial p(x).A polynomial of degree 1 is called a linear polynomial , degree 2 is called quadratic polynomial,degree 3 is called a cubic polynomial.
- If p(x) is a polynomial in x, and if k is any real number, then the value obtained by replacing x by k in p(x), is called the value of p(x) at x = k, and is denoted by p(k).A real number k is said to be a zero of a polynomial p(x), if p(k) = 0

- Check out Polynomial expression Degree,Value,Zeroes for the details on the above
- Polynomials Addition ,Subtraction ,Multiplication and division were also learned. Check out below links

Adding And subtracting Polynomials

Multiplying And Dividing Polynomials - Factoring of Polynomials can be done using grouping,split mid-term method,identity method. This we also learned in earliar classes.Check out How to factor polynomials for details
- This chapter we will focussing on finding the relationship between the coefficients and Zeroes of the polynomials expression. We will also study the division algorithm for polynomial

y= p(x) where p(x) is the polynomial of any form.

Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x and y obtained by putting the values. The plot or graph obtained can be of any shapes

The zero's of the polynomial are the points where the graph meet x axis in the Cartesian plane. If the graph does not meet x axis ,then the polynomial does not have any zero's.

Let us take some useful polynomial and shapes obtained on the Cartesian plane

- If the degree n of a polynomial is even, then the arms of the graph are either both up or both down.
- If the degree n is odd, then one arm of the graph is up and one is down.
- If the leading coefficient an is positive, the right arm of the graph is up.
- If the leading coefficient an is negative, the right arm of the graph is down

These points will help in roughly drawing the graph of any polynomial

P(x)=s(x) q(x) + r(x)

Where r(x) can be zero or degree of r(x) < degree of g(x)

Steps to divide a polynomial by another polynomial

- Arrange the term in decreasing order in both the polynomial
- Divide the highest degree term of the dividend by the highest degree term of the divisor to obtain the first term,
- Similar steps are followed till we get the reminder whose degree is less than of divisor

Divide P(x) by q(x)

$P(x)=x^4 +x +1$

$q(x)=x+1$

Following the step outlined above,here is the division

So $q(x)=x^3-x^2+x$

r(x)=1

So

$x^4 +x +1=(x+1)(x^3-x^2+x)+1$

**Notes****NCERT Solutions****Assignments**

Given below are the links of some of the reference books for class 10 math.

- Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
- Mathematics for Class 10 by R D Sharma
- Pearson IIT Foundation Maths Class 10
- Secondary School Mathematics for Class 10
- Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.

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