Download 8.7 2016-2017

8.7 Factoring ax2 + bx + c
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Essential Question:
What is the process for factoring and solving
ax2 + bx + c = 0?
***WHEN LEAD COEFFICIENT IS NOT = 1
5-Minute
Check 1
Factor m2 – 13m + 36.
A. (m – 4)(m – 9)
B. (m + 4)(m + 9)
C. (m + 6)(m – 6)
D. (m + 6)2
5-Minute
Check 2
Solve y2 – 8y – 20 = 0.
A. {–4, 3}
B. {3, 6}
C. {–2, 10}
D. {1, 8}
Content Standards
A.SSE.3a Factor a quadratic expression to reveal the
zeros of the function it defines.
A.REI.4b Solve quadratic equations by inspection
(e.g., for x2 = 49), taking square roots, completing the
square, the quadratic formula and factoring, as
appropriate to the initial form of the equation.
Recognize when the quadratic formula gives complex
solutions and write them as a ± bi for real numbers a
and b.
Mathematical Practices
4 Model with mathematics.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State
School Officers. All rights reserved.
• prime polynomial
Factor ax2 + bx + c
Steps:
1.
2.
3.
4.
5.
If possible, simply each term (Factor out GCF)
Multiply (a*c) for Step 3
Find 2 Integers that multiply to get (a*c) and add to get b.
1. Set up the T Chart to Find the 2 Integers
Set up factored form ( )( )
1. Don’t forget to add your LEAD COEFFICIENT
Simply each binomial, if possible
CN1. Factor 5x2 + 27x + 10.
Practice 1
Factor 3x2 + 26x + 35.
A. (3x + 7)(x + 5)
B. (3x + 1)(x + 35)
C. (3x + 5)(x + 7)
D. (x + 1)(3x + 7)
2
Factor ax + bx + c
CN2. Factor 4x2 + 24x + 32.
Practice 2
Factor 2x2 + 14x + 20.
A. (2x + 4)(x + 5)
B. (x + 2)(2x + 10)
C. 2(x2 + 7x + 10)
D. 2(x + 2)(x + 5)
Determine Whether a Polynomial is Prime?
CN3. Factor 3x2 + 7x – 5, if possible.
Practice 3
Factor 3x2 – 5x + 3, if possible.
A. (3x + 1)(x – 3)
B. (3x – 3)(x – 1)
C. (3x – 1)(x – 3)
D.
prime
Real Life Application
Solve Equations by Factoring
CN4. ROCKETS
Mr. Nguyen’s science class built a model rocket for a competition. When
they launched their rocket outside the classroom, the rocket cleared the
top of a 60-foot high pole and then landed in a nearby tree. If the launch
pad was 2 feet above the ground, the initial velocity of the rocket was 64
feet per second, and the rocket landed 30 feet above the ground, how
long was the rocket in flight? Use the equation h = –16t2 + vt + h0.
End of lesson
Homework:
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• Write Cornell Notes Summary
• Unit 5 Homework Packet
WHAT TO DO DAILY…
• Review Cornell Notes
• BRING CALCULATORS
• CHECK YOUR MATH CALENDARS