This document provides instructions for factoring quadratic trinomials. It defines quadratic trinomials as expressions of the form ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to 0. It then presents the steps to factor quadratic trinomials where a=1: 1) factor the first term, 2) factor the last term such that the sum of the factors equals the coefficient of the middle term, and 3) write the expression as a product of two binomials. Several examples demonstrating these steps are shown. Factors are checked using the FOIL method. Finally, factors are provided for three additional quadratic trinomials.

1. WELCOME
to
Lyn On Me
Channel!

2. FACTORING
QUADRATIC
TRINOMIALS

3. Quadratic trinomials
is written in the form
ax2 + bx + c, where
a,b,c are real numbers
and a cannot be equal
to zero.

4. Examples of quadratic trinomials
1. x2 + 6x + 8
2. y2 - 8y + 12
a = 1, b = -8, c = 12
3. m2 – 2m – 24
a = 1, b = -2 c = -24
a = 1 b = 6 c = 8

5. HOW DO WE
FACTOR
QUADRATIC
TRINOMIALS?

6. To factor quadratic
trinomials of the form
ax2 + bx + c means to
express the trinomial
as a product of two
binomials.

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.

10. EXAMPLE 1: Factor x2 + 5x + 6.
6 = 1 ● 6
6 = 2 ● 3
1 + 6 = 7
2 + 3 = 5
X

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

26. Find the factors of the following:
1. x2 + 6x + 8 = (x + 2)(x + 4)
2. y2 + 4y – 12 = (y + 6)(y - 2)
3. m2 – 2m – 24 = (m - 6)(m + 4)

27. Thank
you!