polynomials (algebra) - class 10
TRANSCRIPT
POLYNOMIALS(Algebra)
Class – 10Mathematics
Synopsis
• Meaning of polynomial• Examples of polynomial• Examples of non polynomial• Degree of polynomial• Types of polynomial• General form of polynomial• Value of a polynomial at a given point
Meaning - Polynomial
• It is an expression made with constants, variables and exponents which are combined using addition, subtraction and multiplication but not division.
• The exponents can only be 0,1,2,3....etc
• A polynomial cannot have infinite number of terms.
Examples of polynomial
3535 32 YXXY
13456 234 xxxx
53 x
Examples of non polynomial
23 xx
22x
2x
Degree of a polynomial
Highest power of x in P(x). For example:4x+2 is a polynomial in the variable x of degree 1
Tell the degree of the following polynomials;
Answer is 3 because it is the highest degree of the given polynomial.
1234 23 xxx
Types of polynomials
On the basis of degree we have mainly 5 types:1. Constant polynomial of degree 0, for instance:
2. Linear polynomial of degree 1, for instance:
3. Quadratic polynomial of degree 2, for instance
132
u
vvyxx325,2,
5232 222
2x-3, y+2,
1, 2/5, -3
Types of polynomials4. Cubic Polynomial of degree 3, for instance:
5. Bi –quadratic polynomial of degree 4, for instance:
323 3,2 xxx
582 34 xxx
Types of polynomialOn the basis of number of terms, we have 3 types ofpolynomials1. Monomial polynomial wherein only one term exist:
2. Binomial polynomial where only 2 terms exists:
3. Trinomial polynomial where 3 terms exists:
53,257 2 xx
523 2 xx
yx32,7
General form of polynomial
• Linear polynomial:
• Quadratic polynomial:
• Cubic polynomial:
0, abax
0,2 acbxax
0,23 adcxbxax
Value of a polynomial at a given point
If p(x) is a polynomial in x and a is real number. Then the value obtained by putting x=a in p(x) is called the value of p(x) at x=a.
Let its value at x=2 is
Thus, 14 is the value.
245)( 2 xxxp
142820)2(2)2(4)2(5)2( 2
pp
Lesson by:
Anjali Kaur SuriTGT Maths, PGT Economics
M.A. (Economics), M.Com (Finance), PGD Banking & Finance, B.A. Hons (Economics), B.Ed (Maths & SST), NISM, NSDL and IELTS certified.
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