Introduction of Polynomials
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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
be constants. Then,
f(x) = an
+ ... + a1
x + a0
is called a Poly-nomial
in variable x.
, ... , a1
are known as terms
, ..., a1
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
+ 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.
- 3√x + 5
It is not a poly-nomial because the exponent of one term is 1/2 which is less than 1.
- 2x + 5)
It is not a poly-nomial because the exponent is negative.
- 3/x + 4
As the exponent of 2nd term is -1 so it is not a poly-nomial.
Q.1 Write any poly-nomial in x with degree 3.
Q.2 P(x) = x3
- 4x + 8. Write the coefficient of x2
Q.3 In P(x) = 5x2
- 2x + 4 write the degree of poly-nomial.
Q.4 In P(x) = 1/2 x3
+ 8x, state the number of terms and write each terms.
• 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