If the equation is f(x)=2x+5
The domain is 2x+5
If the range is 1, the domain is 7
★ Arithmetic Progression [ Explicit and Recursive notation ] ★
Arithmetic Sequence - 19 , 9 , -1 ...
Recursive Notation -
First term = 19
Common difference = -10
In subscript notation - [ a₁ = 19 , aₙ = aₙ-₁ -10 ]
In functional notation - f(n) = f (n -1) -10
Explicit Notation - f ( n ) = f ( 1 ) + d ( n - 1 )
= 19 - 10 ( n -1 )
= 29 - 10n
It's functional and subscript notations resides the same
Group and factor
undistribute then undistribute again
remember
ab+ac=a(b+c)
this is important
6d^4+4d^3-6d^2-4d
undistribute 2d
2d(3d^3+2d^2-3d-2)
group insides
2d[(3d^3+2d^2)+(-3d-2)]
undistribute
2d[(d^2)(3d+2)+(-1)(3d+2)]
undistribute the (3d+2) part
(2d)(d^2-1)(3d+2)
factor that difference of 2 perfect squares
(2d)(d-1)(d+1)(3d+2)
77.
group
(45z^3+20z^2)+(9z+4)
factor
(5z^2)(9z+4)+(1)(9z+4)
undistribuet (9z+4)
(5z^2+1)(9z+4)
