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

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UHS CST 2012 Absolute Value Simplify Expressions System of Equations Polynomials Polynomials Factoring

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)

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