Table of contents  
Polynomial  
Zeroes or roots of a polynomial  
Relationship between Zeroes and Coefficients of a Polynomial  
Division Algorithm  
Identities of Algebra 
A polynomial is an algebraic expression in which the variables have nonintegral exponents only.
Example 3x^{2}+ 4y + 2, 5x^{3}+ 3x^{2} + 4x +2
For a polynomial in one variable  The highest exponent on the variable in a polynomial is the degree of the polynomial.
Example: The degree of the polynomial x^{2}+3x+4 is 3, as the highest power of x in the given expression is x^{2}.
It is that value of a variable at which polynomial P(x) becomes zero.
Example: if polynomial P(x) = x^{3}6x^{2}+11x6, Putting x = 1 one get P(1) = 0 then 1 is a zero of polynomial P(x).
The division algorithm states that for any given polynomial p(x) and any nonzero polynomial g(x) there are polynomial q(x) are r(x) such that
p(x) = g(x) × q(x) + r(x)
Dividend = Divisor × Quotient + Remainder
Where r(x) = 0 or degree r(x) < degree g(x)
A polynomial of degree n has at most n zeros.
Quadratic polynomials can be factorized by splitting the middle term.
For example, consider the polynomial 2x^{2}−5x+3
Splitting the middle term
The middle term in the polynomial is 5x
Sum = 5
Product = 6
Now, 5 can be expressed as (2) + (3) and 2 x 3 = 6
Putting the above value in the gven expression
2x^{2}−5x+3 = 2x^{2}−2x−3x+3
Identify the common factor
2x^{2}−2x−3x+3 = 2x(x−1)−3(x−1)
Taking (x−1) as the common factor, this can be expressed as:
2x(x−1)−3(x−1)=(x−1)(2x−3)
(a+b)^{2} = a^{2}+2ab+b^{2}
(a−b)^{2}=a^{2}−2ab+b^{2}
(x+a)(x+b) = x^{2}+(a+b)x+ab
a^{2}−b^{2} = (a+b)(a−b)
a^{3}−b^{3} = (a−b)(a^{2}+ab+b^{2})
a^{3}+b^{3} = (a+b)(a^{2}−ab+b^{2})
(a+b)^{3} = a^{3}+3a^{2}b+3ab^{2}+b^{3}
(a−b)^{3} = a3−3a^{2}b+3ab^{2}−b^{3}
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