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Title: Solving Quadratic Equation by Factoring
Description: A discussion on Solving Quadratic Equations by factoring.

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September 21, 2019
Lesson Guide for High School Math in Grade 9
Solving Quadratic Equations by Factoring
1
...
Solve quadratic equation by factoring
Reference/s
1
...
, page 27 – 34
2
...
Andres, et
...
, page 6 - 7
RECALL
DIFFERENT FACTORING TECHNIQUES

1
...
x2 – 36 = (x + 6) ( x – 6)
find the square root of the first term

√𝑥

2

=x

find the square root of the last term

√36

=6

write the factors as sum and difference of two terms, (x + 6)(x – 6)
b
...
PERFECT SQUARE TRINOMIALS
x2 + 2xy + y2 = (x + y) (x + y)
x2 – 2xy + y2 = (x – y) (x – y)
EXAMPLES:
a
...
c2 – 6c + 9 = (c – 3) (c – 3)
1

find the square root of the first term

√𝑐

find the square root of the last term

√9

2

=c
=3

copy the sign of the middle term, in this example -6c is negative
4
...
if a = 1 , find factors of c whose sum is b
EXAMPLES
a
...
x2 + 10x – 24 = (x + 12) (x – 2)

factor of - 24 whose sum is 10 is 12 and -2

c
...
x2 – 4x - 32 = (x – 8) (x + 4)

factor of -32 whose sum is -4 is - 8 and 4

B
...


b
...
Transform the quadratic equation into
standard ax2 + bx + c = 0 form if
necessary
2
...
Apply the zero product property by
setting each factor of the quadratic
expression equal to 0
4
...


(x + 5) ( x – 2) = 0
x+5=0
;
x–2=0
x+5–5=0–5
x = -5
2

; x–2+2=0+2
x=2

Zero Product Property
If the product of two real numbers is zero, then either of the two is equal to zero or
both numbers are equal to zero
...


X ( x – 6) = 0

factor out common monomial factor

;x–6=0

x=0

x

equate the factors to zero

= 6

simplify

checking:
x=0

;

x=6

x2 – 6x = 0

x2 – 6x = 0

02 – 6(0) = 0

62 – 6(6) = 0

0

-0

36 – 36 = 0

=0
0=0

0=0

x2 – 64 = 0

2
...


Write to standard form

x2 – 10x + 25 = 10x – 10x
x2 – 10x + 25 = 0

x–5=0 ;
=5

factor the left side of the equation

x–5=0
;

x

Subtract 10x on both sides of equation
Write to standard form

(x – 5) ( x – 5) = 0

x

x=8

simplify

=5
3

checking:
x=5

;

x=5

x2 + 25 = 10 x

x2 + 25 = 10 x

52 + 25 = 10(5)

x2 + 25 = 10 x

25 + 25 = 50

x2 + 25 = 10 x

50 = 50

4
...


a2 + 13a + 30 = 0

Write the equation to standard form

(a + 10) ( a + 3) = 0

factor out the left side of the equation

a + 10 = 0

equate the factors to zero

a

;

a+3=0

= -10 ;

a

= -3

solve for the variable

checking:
a

= -10 ;

a2 + 13a = - 30
(-10)2 + 13(-10) = -30
100

- 130
- 30

6
Title: Solving Quadratic Equation by Factoring
Description: A discussion on Solving Quadratic Equations by factoring.