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CST Review #1: Absolute Value, Simplify Expressions, System of Equations, Polynomials,Polynomials Factoring

UHS CST 2012 Absolute Value Simplify Expressions System of Equations Polynomials Polynomials Factoring
STUDY
PLAY
Absolute Value
Ex:1--------- | x+ 1|=10
| x+ 1|=10
x+1= 10 x+1= -10
x=9 x=-11
Absolute Value
Ex:2 ---------| x -10 |-18= -8
| x -10 |-18= -8
| x -10 |= 10
x -10 = 10--------- x -10 = -10
x=20---------- x=0
Absolute Value
Ex:3 ---------| 2x-( 4x- 4) |=1
| 2x-( 4x- 4) |=1
| 2x -4x+ 4 |=1
2x -4x+ 4 =1--------- 2x -4x+ 4 = -1
-2x+ 4= 1----------- -2x+ 4= -1
-2x = -3----------- -2x = -5
x= 3/2 -----------x= 5/2
Simplify Expressions
Ex:1 ---------1/2( 2z+ 8y+ 6z)
1/2( 2z+ 8y+ 6z)
1z+ 4y+ 3z
4y + 4z
Simplify Expressions
Ex:2------- 5 x -y/ 10 -x
5 x -y/ 10 -x
5x x/ 10y
x x/ 2y
(the two x's should combine)
Simplify Expressions
Ex:3------(x- 6)(x+ 6)
__| x |_6_
x_| x2 |_6x
6 | 6x |_36
= x2+12x+36-------- [ 2 is an exponent ]
System of Equations
elimination
eliminate one variable (x) and solve for y.
then substitute the y into original equations.
System of Equations
graphed
The point of intersection of the two graphs gives the solution to the system of equations.
The two lines intersect at (-2, 4).
so, x= -2 & y= 4
System of Equations
substitution
2x+ 2y= 10
2x+ y= 10
solve the second equation for x
y= -2x+ 10
now substitute x into the first equation.
2x+ 2( -2x+ 10)= 10
2x- 4x+ 20= 10
-2x= -10
x= 5
Polynomials
6x + 5xy + 3x
6x + 5xy + 3x =
(6x + 3x) + 5x2y =
[when you add # with variables that have exponents. add the numbers but keep the similar variables]
9x + 5xy
Polynomials Factoring
Ex.1--------- x2- 16
x2- 16 [ 2 is an exponent ]
(x- 4)(x+ 4)
Polynomials Factoring
Ex.3 -------- x2- 2x- 8
x2- 2x- 8 [ 2 is an exponent ]
\-2/ (1)(-8),(2)(-4)
/-8\
x=2 x= -4
(x+ 2)(x- 4)
Polynomials Factoring
Ex.3 --------- 5xy+ 10x
5xy+ 10x=
5xy+ (5)(2)x=
5x(y+ 2)