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13 terms

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

Absolute Value

Ex:1--------- | x+ 1|=10

Ex:1--------- | x+ 1|=10

| x+ 1|=10

x+1= 10 x+1= -10

x=9 x=-11

x+1= 10 x+1= -10

x=9 x=-11

Absolute Value

Ex:2 ---------| x -10 |-18= -8

Ex:2 ---------| x -10 |-18= -8

| x -10 |-18= -8

| x -10 |= 10

x -10 = 10--------- x -10 = -10

x=20---------- x=0

| x -10 |= 10

x -10 = 10--------- x -10 = -10

x=20---------- x=0

Absolute Value

Ex:3 ---------| 2x-( 4x- 4) |=1

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

| 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)

Ex:1 ---------1/2( 2z+ 8y+ 6z)

1/2( 2z+ 8y+ 6z)

1z+ 4y+ 3z

4y + 4z

1z+ 4y+ 3z

4y + 4z

Simplify Expressions

Ex:2------- 5 x -y/ 10 -x

Ex:2------- 5 x -y/ 10 -x

5 x -y/ 10 -x

5x x/ 10y

x x/ 2y

(the two x's should combine)

5x x/ 10y

x x/ 2y

(the two x's should combine)

Simplify Expressions

Ex:3------(x- 6)(x+ 6)

Ex:3------(x- 6)(x+ 6)

__| x |_6_

x_| x2 |_6x

6 | 6x |_36

= x2+12x+36-------- [ 2 is an exponent ]

x_| x2 |_6x

6 | 6x |_36

= x2+12x+36-------- [ 2 is an exponent ]

System of Equations

elimination

elimination

eliminate one variable (x) and solve for y.

then substitute the y into original equations.

then substitute the y into original equations.

System of Equations

graphed

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

The two lines intersect at (-2, 4).

so, x= -2 & y= 4

System of Equations

substitution

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

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 + 5xy + 3x =

(6x + 3x) + 5x2y =

[when you add # with variables that have exponents. add the numbers but keep the similar variables]

9x + 5xy

(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

Ex.1--------- x2- 16

x2- 16 [ 2 is an exponent ]

(x- 4)(x+ 4)

(x- 4)(x+ 4)

Polynomials Factoring

Ex.3 -------- x2- 2x- 8

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)

\-2/ (1)(-8),(2)(-4)

/-8\

x=2 x= -4

(x+ 2)(x- 4)

Polynomials Factoring

Ex.3 --------- 5xy+ 10x

Ex.3 --------- 5xy+ 10x

5xy+ 10x=

5xy+ (5)(2)x=

5x(y+ 2)

5xy+ (5)(2)x=

5x(y+ 2)