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