PURE MATH 2
, Chapter 1 :
Algebraic methods
Factor theorem
* f(p) =
0 (x-p) is a factor of f(x)
factor of f(x)
*
+(5) =
0 (ax- b) is a
Remainder theorem
* f(x) is divided by (ax-b) then remainder is
f()
Mathematical proofs
1 Deduction facts to desired results
get
:
using known
of
Ex : Prove that
, product 2 even number is even
In even 2n + 2m = umn =
2x/2mm) v
2n + 1 odd
2 Identities : E
Ex : x2 + 2x = (x 1)
+ -
1
LHS =
X2 + 2X =
(X +
E)2 (E)2 (by
-
completing the square)
=
(x + 1)2 -
1 = RHS
EX : x + 2bX + c = 0 = X = -
bi
LHS = X+ 2bx + c = -
bac (using discriminant
2a
-Lb = 4b2 4c Rb = x
=
b = RHS
-
=
= -
C =
2 2
, Chapter 1 :
Algebraic methods
Factor theorem
* f(p) =
0 (x-p) is a factor of f(x)
factor of f(x)
*
+(5) =
0 (ax- b) is a
Remainder theorem
* f(x) is divided by (ax-b) then remainder is
f()
Mathematical proofs
1 Deduction facts to desired results
get
:
using known
of
Ex : Prove that
, product 2 even number is even
In even 2n + 2m = umn =
2x/2mm) v
2n + 1 odd
2 Identities : E
Ex : x2 + 2x = (x 1)
+ -
1
LHS =
X2 + 2X =
(X +
E)2 (E)2 (by
-
completing the square)
=
(x + 1)2 -
1 = RHS
EX : x + 2bX + c = 0 = X = -
bi
LHS = X+ 2bx + c = -
bac (using discriminant
2a
-Lb = 4b2 4c Rb = x
=
b = RHS
-
=
= -
C =
2 2
