Check HW #4 with answer
keys. Use red pens to check
and correct.
Turn in Homework and
answer keys with your
group. (Person wearing the
most red.)
Work on the opener.
Chapter Six
Section 6.5
Opener/Notes #5
Work on the “Opener”
problems with your group.
Opener Solutions:
1) (x - 4)(x - 2)
2) x(x + y + 3)
3) a2(a2 + ab + b2)
4) (d-3)(d2 + 3d + 9)
5) (3y + 2)(y + 1)
6) 3(d - 4)(d + 4)
7) 3(2d - 3)(d + 7)
8) (2y - z)(2y + z)(4y2 + z2)
9) (4m + 5)(16m2 - 20m + 25)
Target Goal:
• Solve Polynomial Equations by Factoring (#5)
D: Quadratic Equation
ax2 + bx + c = 0
where a, b, c,
≠0
€
and a, b, c are
integers
(NO fractions)
Degree of Quadratic Equations (Non-linear)
Degree of 2
⇒ at most 2 solutions
€
Degree of
3
⇒ at most 3 solutions
€
Degree of
4
⇒ at most 4 solutions
€
and so on
D: Roots or solutions
• the x-intercepts of the graph
• called the “zeros” of the equation
Zero Product Property:
If ab = 0 then either a = 0 or b = 0.
ex. If (x +2)(x+3) = 0
then either
x + 2 = 0 or x + 3 = 0
which means
x = -2 or x = -3
Target Goal:
• Solve Polynomial Equations by Factoring (#5)
Solve
• Factor
Example One:
x 2 −2x−15=0
• Set each factor = 0
• Solve the 2 equations.
• This equation crosses
the x-axis 2 times.
• Check on Calc
€
(x−5)(x+3)=0
x−5=0
x+3=0
x=5 or x=−3
Solve
• Set equation = 0
• Factor
Example Two:
x 2 +6x=−9
(perfect square
trinomial)
x 2 +6x+9=0
• Set the factor = 0
(x+3)(x+3)=0
• Solve the equation.
x+3=0
• This equation touches
the x-axis 1 time.
x=−3
€
• Check on Calc
Solve
• Set equation = 0
• Factor
Example Three:
a 3 =81a
(GCF and difference
of 2 squares)
a 3 −81a=0
• Set each factor = 0
a(a 2 −81)=0
• Solve each equation.
a(a−9)(a+9)=0
• This equation crosses
the x-axis 3 times.
• Check on Calc--use
zoom fit
a=0
€
a=9
a=−9
Solve
• Set equation = 0
• Factor
Example Four:
3x 2 −6x=9
(GCF and trial and
3x 2 −6x−9=0
error)
• Divide each side by 3
3(x 2 −2x−3)=0
• Set each factor = 0
3(x−3)(x+1)=0
• Solve each equation.
(x−3)(x+1)=0
• This equation crosses
the x-axis 2 times.
Check on Calc.
€
x−3=0
x+1=0
x=3
x=−1
Do examples 5 and 6 with your group.
Example Five:
Example Six:
12x 2 −7x−10=0
x(42x 2 −55x+8)=0
(3x+2)(4x−5)=0
x(6x−1)(7x−8)=0
3x+2=0
x=0 6x−1=0 7x−8=0
4x−5=0
x=0, 1 , 8
6 7
x=− 2, 5
3 4
€
€
Target Goal:
• Solve Polynomial Equations by Factoring (#5)
Homework #5
Worksheet
See board for ch. 6 test date