- 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
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- Dividing Polynomails
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- How to factor polynomials
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- Solved Examples Polynomials
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The value of constant remains same throughout the case and it does not changes in the given situation. They are generally denoted by a,b,c etc

Variable value keep changing and they are generally denoted by the letters x,y,z etc

A polynomial expression S(x) in one variable x is an algebraic expression in x term as

S(x)=a

Where a

1) a

2) n is called the degree of the polynomial

3) when a

4) A constant polynomial is the polynomial with zero degree, it is a constant value polynomial

5) A polynomial of one item is called monomial, two items binomial and three items as trinomial

6) A polynomial of one degree is called linear polynomial, two degree as quadratic polynomial and degree three as cubic polynomial

We can also have polynomials in more than one variable. For example, x^{2} + y^{2} +z^{2} (where variables are x, y and z) is a polynomial in three variables. Similarly p^{2} + q^{4} + r (where the variables are p, q and r) is polynomials in three variables

Also if a_{0} = a_{1} = a_{2} = a_{3} = . . . = a_{n} = 0 (all the constants are zero), we get the zero polynomial, which is denoted by 0. Now we may ask What is the degree of the zero polynomial? The degree of the zero polynomial is not defined

Also if a

The degree of a term is the sum of the exponents of the variables that appear in it

Lets take a example of polynomial

S(x) =x^{3} +x^{2}+ 5

Here the highest exponent of x is 3. So degree of the polynomail is 3

Similarly

We have polynomial types depending on degree also

For constant polynomial

P(x) = 9

It can be expression as

P(x) =9x^{0}

So degree is zero

S(x) =x

Here the highest exponent of x is 3. So degree of the polynomail is 3

Similarly

Polynomial |
Degree of the polynomial |

4x +1 |
1 |

3x^{2} + 4x+6 |
2 |

9x^{3} -4x^{2} +1 |
3 |

x^{5} -x+1 |
5 |

We have polynomial types depending on degree also

Polynomial |
Degree of the polynomial |
Polynomial type |

4x +1 |
1 |
Linear polynomial |

3x^{2} + 4x+6 |
2 |
Quadratic Polynomial |

9x^{3} -4x^{2} +1 |
3 |
Cubic Polynomial |

x^{4} -x+1 |
4 |
Quartic Polynomial |

5x^{5} -x+1 |
5 |
Quintic Polynomial |

For constant polynomial

P(x) = 9

It can be expression as

P(x) =9x

So degree is zero

Lets take a example of polynomial

S(x) =x

Then

When we put the value of x=2,then

S(2)=4+1=5

The S(2) is the called the value of polynomial at x=2

In General terms, the value of polynomial at x=a is S(a)

It is a solution to the polynomial equation S(x)=0 i.e. a number "a" is said to be a zero of a polynomial if S(a) = 0.

If we draw the graph of S(x) =0, the values where the curve cuts the X-axis are called Zeros of the polynomial

a) Linear polynomial has only one root

b) A zero polynomial has all the real number as roots

c) A constant polynomial has no zeros

d) A zero of polynomial need not to be 0

Check out the below video for Polynomial

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