Download 5.2: Solving Quadratic Equations by Factoring - Winterrowd-math

5.2: Solving Quadratic
Equations by Factoring
(p. 256)
How do you factor:
x2 +bx +c
ax2+bx+c
a2 −b2
a2 +2ab +b2
a2 −2ab +b2
How do you solve a quadratic function?
Everything you ever learned about
factoring in one section!
To solve a quadratic eqn.
by factoring, you must
remember your factoring
patterns!
Zero Product Property
• Let A and B be real numbers or algebraic
expressions. If AB=0, then A=0 or B=0.
• This means that If the product of 2 factors
is zero, then at least one of the 2 factors
had to be zero itself!
Example: Solve.
x2+3x-18=0
x2+3x-18=0
(x+6)(x-3)=0
x+6=0 OR x-3=0
-6 -6
+3 +3
x=-6 OR x=3
Factor the left side
set each factor =0
solve each eqn.
check your solutions!
Example: Solve.
2t2-17t+45=3t-5
2t2-17t+45=3t-5
2t2-20t+50=0
2(t2-10t+25)=0
t2-10t+25=0
(t-5)2=0
t-5=0
+5 +5
t=5
Set eqn. =0
factor out GCF of 2
divide by 2
factor left side
set factors =0
solve for t
check your solution!
Example: Solve.
3x-6=x2-10
3x-6=x2-10
0=x2-3x-4
0=(x-4)(x+1)
x-4=0 OR x+1=0
+4 +4
-1 -1
x=4 OR x=-1
Set = 0
Factor the right side
Set each factor =0
Solve each eqn.
Check your solutions!
Example: Factor 3x2 −17x+10
1. 3x2 −17x+10
2. 3x2 −?x −?x+10
1. Factors of (3)(10) that
add to −17
2. Factor by grouping
3. 3x2 −15x −2x+10
3. Rewrite equation
4. 3x(x−5)−2(x−5)
4. Use reverse
distributive
5. (x−5)(3x−2)
5. Answer
Example: Factor 3x2 −17x+10
1. 3x2 −17x+10
2. 3x2 −?x −?x+10
3.
x
−5
3x
3x2
−15x
−2
−2x
+10
1.Rewrite the equation
2. Factors of (3)(10)
that add to −17 (−15 &
−2)
3. Place numbers in a
box
4. Take our common
factors in rows.
5. Take our common
factors in columns.
Finding the Zeros of an Equation
• The Zeros of an equation are the xintercepts !
• First, change y to a zero.
• Now, solve for x.
• The solutions will be the zeros of the
equation.
Example: Find the Zeros of
y=x2-x-6
y=x2-x-6
0=x2-x-6
0=(x-3)(x+2)
x-3=0 OR x+2=0
+3 +3
-2 -2
x=3 OR x=-2
Change y to 0
Factor the right side
Set factors =0
Solve each equation
Check your solutions!
If you were to graph the eqn., the graph would
cross the x-axis at (-2,0) and (3,0).
Assignment
p. 260, 23-31 odd
35-43 odd,
47-51 odd,
57-69 odd