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Polynomials, Polynomials - Coggle Diagram
Polynomials
P(x)=8x⁵+2x⁴+x-21
Leading coefficient=8
Coeffficients=8,2.1,--21
Constant term=--21
Degree=5
The most common type of algebraic expression
Constant Polynomials
The degree of a constant polynomials is zero
5x ^ n-4/7 → n-4/7=0 n=4
Sum of the coefficient
We substitute 1 for each variable
P(x+3)=P(4)
Q(x²+5x-1)=Q(15)
P(x),Q(x),R(x)
These are used to show polynomails with variable x
Power of x must be natural numbers
Polynomials
Zero Polynomials
P(x)=0
All elements of each polynomials must be zero
Q(x)=(n+6).x²+ k.x+m+t-10
n=--6 k=0 m+t-10=0
Constant Term
We substitute zero for each variable
P(x)=P(0)
P(x+3)=P(3)
Operations on Polynomials
If m>n
d [P(x) + Q(x)]=m
d [P(x) . Q(x)]=m+n
d [P(x) / Q(x)]=m-n
Equal Polynomials
P(x)=Q(x)
That means equal polynomials
Division On Polynomials
P(x)=Q(x).B(x)+K(x)
If K(x) is 0 it is divided without remainder
P(x)=x³-2x²+6x-5 divided by (x-1)
x-1=0 then x=1
1-2+6-5=0 remainder is 0
