Polynomials 6.17 Factor Trinomial Equations Coeffient Greater Than 1.notebook
Factoring Trinomials: ax2 + bx + c
Polynomials
• I can solve equations of the form ax + bx + c
2
TEKs
10.E ­ Factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two (2y + 1) (y - 2)
(2y + 2) (y - 1)
Title Page
1. (2x + 1) (x ­ 2)
2. (3m + 1) (m ­ 3)
3. (4r ­ 1) (4r ­ 1)
4. (2x + 3) (3x ­ 2)
5. (3x ­ 4) (x + 2)
6. (3x ­ 5) (6x + 1)
7. (2a + 3) (a + 1)
8. (6y + 5) (3y ­ 1)
9. (4c ­ 7) (3 ­ c)
10. (4x ­ 8) (2x + 3
11.
12.
13.
14.
15.
16.
17.
18.
19.
(2p + 5) (14p ­ 5)
(6x + 5) (8x ­ 3)
3(y + 2) (y ­ 4)
2(x + 8) (2x ­ 3)
4(2m ­ 3) (m ­ 4)
prime
2(a2 ­ 7a + 9)
prime
30 yds x 10 yds
answer
(2y - 1) (y + 1)
(2y + 1) (y - 1)
ANSWERS
1. (2x + 1)(x + 2)
2. (3n + 2)(n + 1)
3. (2s ­ 1)(s + 5)
4. (3g ­ 1)(g ­ 2)
5. (2t ­ 5)(t ­ 3) 6. B
Warm Up
Practice Answers
Maintain Your Skills
1. A
2. D
Homework Answers
What is the Zero Product Property?
Practice Worksheet
Math
Humor
How does it help solve trinomial equations?
(x ‐ 3) (x + 4) = 0
x‐3=0 x+4=0
Introduction
Math Humor
1
Polynomials 6.17 Factor Trinomial Equations Coeffient Greater Than 1.notebook
_____ Solving Equations by Factoring
Date
1. What is factor • terms with common factors
by grouping?
grouped together
•
•
change to the form a(c+d) + b(c+d)
ax2 + bx + c
2. Coefficient of a is greater • multiply a and c (MAC)
than 1?
• find two numbers that have
~sum equal to b and product
& sum
~product equal to ac
(MAC)
• change to the form
(ax2 + bx) + (bx + c) • factor by grouping
use FOIL to check
Notes
3. What are the steps to solve equations?
•
Notes
factor the trinomial
~look for GCF!
•
•
Find a friend and tell them how to factor a trinomial.
set each factor equal to zero & solve ~usually has two solutions
check solution
Notes
Find a Friend
Examples
Be the only one that the teacher calls on...
Factors of ­72 Sum
Solve the equation.
have to do everyone else's homework?
(MAC)
1. 9p2 + 6p ­ 8 = 0
answer
­1, 72
­72, 1
­2, 36
­36, 2
­3, 24
­24, 3
­4, 18
­18, 4
­6, 12
­12, 6
­8, 9
­9, 8
71
­71
34
­34
21
­21
14
­14
6
­6
1
­1 {2/3, ­4/3} multiply ac to get ­72
what 2 number multiply to get 72 and add to get 6? (6,12)
change to 9p2 ­ 6p + 12p ­ 8
factor by grouping (9p2 ­ 6p) (12p ­ 8)
3p(3p ­ 2) 4(3p­2)
(3p + 4) (3p ­ 2) Set factors equal to 0
Would You Rather?
Examples
2
Polynomials 6.17 Factor Trinomial Equations Coeffient Greater Than 1.notebook
Factors of 36 Sum
Solve the equation
(MAC)
2. 6q ­ 13q = ­6
2
answer
­1, ­36
1, 36
­2,­18
2, 18
­3, ­12
3, 12
­4, ­9
4, 9
­6, ­6
6,6
­37
37
­20
20
­15
15
­13
13
­12
12
Solve the equation.
(MAC)
3. 10w2 ­ 19w = 15 {2/3, 3/2} answer
{5/2, ­3/5} what 2 numbers multiply to get ­150 and add to get ­19? (6,­25)
what 2 numbers multiply to get 36 and add to get ­13? (­4,­9)
change to 10w2 + 6w ­ 25w ­ 15
change to 6q2 ­ 4q ­ 9q + 6
factor by grouping (10w2 + 6w) (­ 25w ­ 15)
factor by grouping (6q2 ­ 4q) (­9q + 6)
2w(5w + 3) ­5(5w + 3)
2q(3q ­ 2) ­3(3q ­ 2)
(5w + 3) (2w ­ 5) Set factors equal to 0
(2q ­ 3) (3q ­ 2) Set factors equal to 0
Examples
Examples
Solve the equation.
Factors of 3 Sum
(MAC)
1, 3
­1, ­3
4
­4
Application
Find the Error!
Dasan and Craig are factoring 2x2 + 11x + 18. Who is correct?
Don't forget...
GCF > 1
Dasan
Craig
Factors of 18 Sum
Factors of 36 Sum
1, 18 19
3, 6 9
9, 2 11
2x2 + 11x + 18
1, 36 37
2, 18 20
3, 12 15
4, 9 13
6, 6 12
2(x2 + 11x + 18)
2x2 + 11x + 18
2 (x+9)(x+2)
Prime Polynomial
answer
answer
Find the Factors!
Factors of Sum
149
­149
73
­73
47
­47
27
­27
19
­19
multiply ac to get ­150
multiply ac to get 36
Examples
­1, 150
1, ­150
­2, 75
2, ­75
­3, 50
3, ­50
­5, 30
5, ­30
­6, 25
6,­25
subtract 15 from both sides
add 6 to both sides
4. 6h2 + 8h + 2 = 0 Factors of ­150 Sum
{­1, ­1/3} Craig; need to find the factors of ac, not just c.
Application
Fun Fact of the Day!
Chicago is known as the Windy City, but this name was not coined from the weather. It was given to the city because of all the wind that politicians were blowing around!
Practice
Factor Trinomial Equations
(Coefficient Greater than 1)
Worksheet
Activity
Homework
3
Polynomials 6.17 Factor Trinomial Equations Coeffient Greater Than 1.notebook
Closing Questions
How do you know if you need to find a solution? Equation
What do you look for first thing when looking at trinomial? GCF
Closing Questions
4