§5.6 Roadmap
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Notes
§5.6 Examples
§5.4, 5.5 Homework Questions
Exam Review Problems
§6.1
Volunteer to solve board problems.
(Math 1010)
M 1010 §5.6
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§5.6 Assignment
Notes
For Wednesday:
1. Exercises from 5.6
2. Next Exam: October 30 - Chapter 4 & 5, and
Cumulative Portion
Study guide: Chapter 4 Test, p 294, # 1 - 5.
Chapter 5 Test, p 367 # 1 - 19.
Cumulative: Chapter 1 - 4, p 295, # 1 - 8, 11 - 20.
(Math 1010)
M 1010 §5.6
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§5.6
Notes
Today’s lesson is using factoring to solve a polynomial equation. The steps
are
1. ”Solve the equation for zero,” or set all terms on one side and zero on
the other.
2. Simplify the equation.
3. Factor the polynomial into smaller factors.
4. Solve each factor equal to zero.
5. Check the solutions in the original equation.
(Math 1010)
M 1010 §5.6
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§5.6 Solving Linear Equations
Notes
We will often need to solve linear equations (§2.1) in later steps. Here are
some examples to try:
(A) x + 1 = 0
(B) 2y − 7 = 0
(C) 6 − s = 0
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Answers: (A) x = −1, (B) y = , (C) s = 6
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M 1010 §5.6
(Math 1010)
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§5.6 Factoring Review
Notes
Factoring will also be a required step. Here are the three basic techniques:
Factoring monomials Find the largest common coefficient and largest
power of the unknown.
6x 4 y 3 + 12x 2 y − 2x 5 y 2 = 2x 2 y (3x 2 y 2 + 6 − x 3 y )
Grouping Factor out common monomials from pairs of terms.
2y 2 (y 2 + 6) + 7(y 2 + 6)
Factoring Trinomials This method uses guessing-and-checking.
(Math 1010)
2
4x 2 + 5x − 6 M=1010
4x§5.6
− 3x + 8x − 6
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§5.6 Zero-Factor Property
Notes
If a · b = 0, then either a = 0 or b = 0. This also applies to three or more
factors.
Example: Solve
x(x − 4) = 0
Either x or (x − 4) must be zero. Setting the second equal to zero gives
x −4=0
x = 4 Add 4 to both sides
The equation x(x − 4) = 0 has exactly two solutions. Check:
x = 0: 0(0 − 4) = 0.
x = 4: 4(4 − 4) = 4(0) = 0.
(Math 1010)
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§5.6 Examples - Quadratic Equations
Notes
Solve:
(A) Example 1 x 2 − x − 6 = 0
(B) Example 2 2x 2 + 5x = 12
(C) Example 3 x 2 − 2x + 16 = 6x
(D) # 25 x 2 − 3x − 10 = 0
(E) #47 x(x − 5) = 36
(F) #57 (t − 2)2 = 16
(Math 1010)
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§5.6 Examples - Higher-Degree Polynomials
Notes
Look for common monomial factors. Look for pairs for grouping.
Solve:
(A) Example 5 3x 3 = 15x 2 + 18x
(B) Example 6 x 4 + x 3 − 4x 2 − 4x = 0
(C) #65 x 3 − 19x 2 + 84x = 0
(D) #69 z 2 (z + 2) − 4(z + 2) = 0
(Math 1010)
M 1010 §5.6
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Notes