7. To factor quadratic trinomial where
a = 1, you can follow the following
steps.
1. Factor the first term.
2. Factor the last term such that
the sum of the factors is equal to
the numerical coefficient of the
middle term.
3. Write as a product of two
binomials.
8. EXAMPLE 1: Factor x2 + 5x + 6.
Step 1
Factor the first term.
= ( x )( x )x2
9. EXAMPLE 1: Factor x2 + 5x + 6.
Step 2
Factor the last term such that the
sum of the factors is equal to the
numerical coefficient of the middle
term.
11. EXAMPLE 1: Factor x2 + 5x + 6.
Step 3
Write as a product of two binomials.
x2 + 5x + 6 = ( _______)( ______)
x2 = (x)(x) = ( x )( x )
6 = (2)(3) = ( +2 )( +3 )
x2 + 5x + 6 = ( x + 2 )( x + 3 )
12. EXAMPLE 1: Factor x2 + 5x + 6.
Check the factors using FOIL METHOD.
( x + 2 )( x + 3 )
13. EXAMPLE 1: Factor x2 + 5x + 6.
Step 4 Check the factors using
FOIL METHOD
( x + 2 )( x + 3 )
= x2 + 5x + 6
= X2 +3X
+2X + 6
14. EXAMPLE 2: Factor y2 - 7y + 10.
Step 1
Factor the first term.
y2 = ( y )( y )
15. EXAMPLE 1: Factor y2 - 7y + 10
Step 2
Factor the last term such that the sum
of the factors is equal to the numerical
coefficient of the middle term.
10 = 1 ● 10
10 = 2 ● 5
X
X
1 + 10 = 11
2 + 5 = 7
16. EXAMPLE 2: Factor y2 - 7y + 10
Step 2
Factor the last term such that the sum
of the factors is equal to the numerical
coefficient of the middle term.
10 = (-1) (-10)
10 = (-2) (-5)
(-1) + (-10) = -11 X
(-2) + (-5) = -7
17. EXAMPLE 2: Factor y2 - 7y + 10.
Step 3
Write as a product of two binomials.
y2 - 7y + 10 = ( )( )
y2 = (y)(y) = ( y )( y )
10 = (-2)(-5) = ( -2 )( -5 )
y2 - 7y + 10 = ( y - 2 )( y - 5 )
18. EXAMPLE 2: Factor y2 - 7y + 10
Check the factors using FOIL METHOD.
( y - 2 )( y - 5 )
= y2 -7y + 10
= y2 -5y
-2y + 10
19. EXAMPLE 3: Factor a2 - 3a - 18
Step 1
Factor the first term.
a2 = ( a )( a )
20. EXAMPLE 3: Factor a2 - 3a - 18
Step 2
Factor the last term such that the
sum of the factors is equal to the
numerical coefficient of the middle
term.
21. EXAMPLE 3: Factor a2 - 3a - 18
-18 = (-1)(18)
(-2)(9)
(-3)( 6)
-1 + 18 = 17 X
-2 + 9 = 7 X
-3 + 6 = 3 X
1 + (-18 ) = -17 X
2 + (-9 ) = -7 X
3 + (-6) = -3
(1)(-18)
(2)(-9)
(3)(-6)
22. EXAMPLE 3: Factor a2 - 3a - 18.
Step 3
Write as a product of two binomial.
a2 - 3a - 18 = ( )( )
a2 = (a)(a) = ( a )( a )
-18 = (3)(-6) = ( 3 )( -6 )
a2 - 3a - 18 = ( a + 3 )( a - 6 )
23. EXAMPLE 3: Factor a2 - 3a - 18.
Check the factors using FOIL METHOD.
( a + 3 )( a - 6 )
= a2 - 3a - 18
= a2 -6a
+3a -18
24. Examples of quadratic trinomials
1. x2 + 6x + 8
2. y2 - 8y + 12
a = 1, b = -8, c = 12
3. x2 – 2x – 24
a = 1, b = -2 c = -24
a = 1 b = 6 c = 8
25. Find the factors of the following:
1. x2 + 6x + 8
2. y2 - 8y + 12
3. m2 – 2m – 24