Formula Sheet: Polynomials | Mathematics for ACT PDF Download

 Page 1


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Page 2


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2
Page 3


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2 3
Page 4


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2 3
Relation between coefficient and zeros of the polynomial: 
Formation of polynomial when the zeroes are given: 
4
Page 5


CHAPTER – 2 
POLYNOMIAL EXPRESSIONS 
A polynomial expression S(x) in one variable x is an algebraic expression in x term as 
? ?
12
1 2 0
............
n n n
n n n
S x a x a x a x ax a
??
??
? ? ? ? ? ?
Where 
10
, ,....... ,
nn
a a a a
?
 are constant and real numbers and 
n
a is not equal to zero.
Some Important points to Note: 
Important Concepts on Polynomial: 
1
Geometric Meaning of the Zeroes of the Polynomial: 
Let’s  us assume 
Y= p (x) where p(x) is the polynomial of any form. 
Now we can plot the equation y=p(x) on the Cartesian plane by taking various values of x 
and y obtained by purring the values. The plot or graph obtained can be of any shapes. 
The zeroes of the polynomial are the points where the graph meet x axis in the Cartesian 
plane. If the graph does not meet x axis, then the polynomial does not have any zero’s. 
Let us take some useful polynomial and shapes obtained on the Cartesian plane 
2 3
Relation between coefficient and zeros of the polynomial: 
Formation of polynomial when the zeroes are given: 
4
Division algorithm for polynomial: 
Let’s p(x) and q(x) are any two polynomial with q(x) ?0, then we can find polynomial s(x) 
and r(x) such that 
P(x) = s(x) q(x) + r(x) 
Where r(x) can be zero or degree of r(x) < degree of g(x) 
  Dividend = Quotient ? Divisor + Remainder