Download 11-3-15 P.7 Alg M1L17 Equation Involving Factored Expressions

11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Date:
Lesson 17:
Equations Involving Factored Expressions
Nov 14­9:09 AM
Do Now:
Factor using the Greatest Common Factor method:
3y2 + 12y
3x(x – 4) + 6(x – 4)
Factor using the Difference of Perfect Squares method:
m2 – 9
x4 ­ 16
Oct 16­6:32 PM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Discuss...
If I told you that the product of two
numbers is 20, could you tell me anything
about the two numbers?
Would the numbers have to be 4 and 5?
Would both numbers have to be
smaller than 20?
Would they both have to be positive?
Nov 14­9:11 AM
If I told you that the product of two
numbers is zero, could you tell me anything
about the two numbers?
How could we phrase this mathematically?
This is known as the zero-product property.
Nov 14­9:14 AM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Example 1
Consider the equation (x−4)(x+3) = 0.
Rewrite the equation as a compound statement.
Find the two solutions to the equation.
Nov 14­9:16 AM
Example 2
Remember to factor prior to solving!
Rewrite the equation as a compound statement.
Solve for x.
2x2 − 10x = 0,
Nov 14­9:18 AM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Example 3
Remember to factor prior to solving!
Rewrite the equation as a compound statement.
Solve for x.
x(x−3) + 5(x−3) = 0
Nov 14­9:21 AM
Example 4
Verify:
(a − 5)(a + 5) = a2 - 25
Nov 14­9:21 AM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Example 5
Solve for x.
x2 - 9 = 5(x - 3)
Nov 14­9:21 AM
Example 6
Notice how these 3 equations are related!
Everyone
Solve for x.
x + 2 = 5
Team 1
Solve for x.
x2
+
2x = 5x
Team 2
Solve for x.
x(5x - 20) + 2(5x - 20) = 5(5x - 20)
Nov 14­9:21 AM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Example 7
Consider the equation (x−2)(2x−3)=(x−2)(x+5).
Lulu chooses to multiply through by 1 and gets the answer
x−2
x = 8.
But Poindexter points out that x=2 is also an answer, which
Lulu missed.
What‛s the problem with Lulu‛s approach?
(x−2)(2x−3)=(x−2)(x+5)
Nov 14­9:29 AM
Use factoring to solve the original equation for x.
(x−2)(2x−3)=(x−2)(x+5)
Nov 14­9:31 AM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Homework:
Exercises 1–6
1) (x+1)(x+2) = 0
3)
2)
(3x−2)(x+12) = 0
(x−3)(x−3) = 0
Nov 14­9:22 AM
Homework continued:
4)
(x+4)(x-6)(x-10) = 0
6)
x(x−5) + 4(x−5) = 0
5)
x2 − 6x = 0
Nov 14­9:27 AM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Exercises 7–9
Use factoring to solve the equation for x:
7)
(x – 2)(2x – 3) = (x – 2)(x + 1).
Nov 14­9:32 AM
8)
Solve for w:
(w+2)(w−5) = w2 − 4.
Oct 26­8:41 PM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
9)
Solve for x:
x2 + 2x = 5x
Nov 14­9:35 AM
10)
The square of a number plus 3 times the number is equal to 4. What is the number?
Oct 26­8:43 PM
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11­3­15 P.7 Alg M1L17 Equation Involving Factored Expressions.notebookNovember 05, 2015
Nov 14­1:00 PM
Oct 26­8:43 PM
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