2. Polynomial
A Polynomial is defined
as a single terms or a sum of a finite number of
terms. In mathematics, a polynomial is an
expression consisting of variables (or
indeterminates) and coefficients, that involves
only the operations of addition, subtraction,
multiplication, and non-negative integer
exponents. Polynomials appear in a wide
variety of areas of mathematics and science
3. LIKE TERMS
"Like terms" are terms whose variables are the same. In other
words, terms that are "like" each other.
Example:
7x x -2x
Are all like terms because the variables are all x.
Add like terms together to make one term:
Example:
7x + x
They are both like terms, so you can just add them:
7x + x = 8x
4. Polynomial Addition
Sum of two polynomials, we need only
add the coefficient of equal powers. The constant terms
should also be added. Adding polynomials is just a
matter of combining like terms, with some order of
operations considerations thrown in.
Eg: Simplify (2x + 3) + (4x + 6)
= 2x + 3 + 4x + 6
= 2x+4x+9
=6x+9
5. Polynomial Subtraction
Difference of two polynomial, we need only subtract
the
coefficient of equal powers.To subtract two
polynomials subtract like terms.
Eg : Simplify (2x + 3) – (4x+6)
= 2x+3-4x-6
= (2x-4x)+(3-6)
= -2x-3
=-(2x+3)
6. POLYNOMIAL
MULTIPLICATION
To multiply polynomial ,multiply each term of
the first polynomial by each term of the second polynomial and
then combine like terms
Example:
(2x+5)(4x-3)=(2xx4x)+(2x x-3)+(5x4x)+(5x-3)
=8x²+6x+20x+15
=8x²+26x+15
7. MULTIPLICATION AND ADDITION
For any three numbers x,y,z , xz+yz=(x+y)z
If there is a common polynomial among these then there is no
need to multiply twice and add .
Example:
(2x+1)(3x+4)+(4x+3)(3x+4)
here the polynomial (3x+4)is common for both
=((2x+1)+(4x+3))(3x+4)
=(6x+4)(3x+4)
=18x²+24x+12x+16
=18x²+36x+16
8. Degree of polynomial
The degree of polynomial is the largest exponent
occuring in its terms.
Eg : 8x²+ 3x + 4
Degree of polynomial = 2
A polynomial whose degree ‘ 1’ is
called first degree polynomial, a polynomial
whose degree ‘ 2’ is called second degree
polynomial.
9. Conclusion
Polynomials are one of the
most important topics in mathematics. For this reason,
it is important that you learn polynomials well.
Moreover, polynomials are great ways to develop a
particular thinking skill. Polynomials should be
studied both because they are one of the most
frequently discussed objects in mathematics and
because they are one of the most interesting.
