Factoring Practice
Find the factors and solutions
x  2 x  35  0
25 x  1  0
3x  x  2  0
9x  6x  0
2
2
2
2
x  2 x  35  0
25 x  1  0
( x  5)( x  7)
(5 x  1)(5 x  1)
{5, 7}
1 1
{ , }
5 5
2
3x  x  2  0
(3x  2)( x  1)
2
2
{ ,1}
3
2
9x  6x  0
3x(3x  2)
2
2
{0,  }
3
Announcements
• Quiz next class over WS 7-3/7-4/7-5
• Factoring Quiz #5 on Friday
Multiply with FOIL
( x  2)( x  2)
x 2x 2x 4
2
x  4x  4
2
Solving Equations that contain
Radicals and Rational Exponents
Objectives
• I can solve equations containing radicals
• I can solve equations containing rational
exponents
• I can determine if a solution is Extraneous
Solving Radical Equations
•
•
•
•
Follow the same rules as any equation
Variable on left
Numbers on Right
Check your answers
Undoing A Radical
•
•
•
•
We undo addition with subtraction
We undo multiplication with division
How do we undo a radical?
We take it to the Power of the Index Number!!
Undoing Radicals
2x  1
( 2 x  1)
2
( 3x  2 )
3
3x  2
( 6x  5)
4
6x  5
3
4
Radical Equations
• When solving radical equations make sure
only the radical is on the left when you
start the problem. (This is like solving
absolute value)
• ALWAYS Check answers. You may get
Extraneous Solutions from radicals.
Example 1
2x  8  5  1
2x  8  6
( 2x  8)  6
2
2x  8  36
2 x  28
x  14
2
Example 2
x 1  3  6
3
3
x 1  3
( 3 x  1) 3  3 3
x  1  27
x  28
Example 3
x  4  4 1
x  4  3
( x  4)  (3)
2
x49
x5
Extraneous
2
Example 4
( x  6)  0 ( x  1)  0
x 3  x 3
x  3  ( x  3)
2
x  3  ( x  3)( x  3)
x  3  x 2  3x  3x  9
x  3  x  6x  9
2
0  x  7x  6
2
0  ( x  6)( x  1)
x6
x  1 Extraneous
Example 5
• .
2x  6  x  3
( 2x  6 )  ( x  3)
2
2x  6  x  3
x6  3
x9
2
Undoing Rational Exponents
• We undo a rational exponent by using the
Reciprocal of that exponent
Undoing Rational Exponents


2
x

1

 


2
3
4


5
3
x

4




3
2
5
4
2x  1
3x  4
EXAMPLE 4
Solve an equation with a rational exponent
Solve (x + 2)3/4 – 1 = 7.
(x + 2)3/4 – 1 = 7
(x + 2)3/4 = 8
(x +
2)3/4
4/3
= 84/3
Write original equation.
Add 1 to each side.
Raise each side to the power 4 .
3
x + 2 = (23)4/3
Apply properties of exponents.
x + 2 = 24
Simplify.
x + 2 = 16
Simplify.
x = 14
Subtract 2 from each side.
Homework
• Worksheet 7-5