Transcript 6.4 Factoring Trinomials

6.4 Factoring Trinomials
Day 1
Factoring Check List
• Factor out the GCF (6.1)
• If there are 2 terms see if it is the Difference of
Two Squares (6.2)
• If there are 3 terms see if it is a Trinomial
Square (6.3)
• If there are 3 terms and it is NOT a Trinomial
Square then we are going to Factor (6.4)
Factoring Trinomials
• To factor three terms you break it down to
two binomials
x²+x +c = (x + __) (x+ __)
x  x  C  ( x  __)( x  __)
4
2
2
2
x  xy  y  ( x  __ y)(x  __ y)
2
2
To find the missing spots
• Make a X
• Put the last term in the
North of the X
• Put the middle coefficient
in the South of the x
• Find two numbers that multiply to the North
and add to the South number
• Put those numbers in the east and west
Factoring Trinomials
• To factor three terms you break it down to
two binomials
x²+x +c = (x + east) (x+ west)
x  x  C  ( x  east )( x  west )
4
2
2
2
x  xy  y  ( x  east _ y)( x  west _ y)
2
2
Example 1: Factor x²+8x+15
15
5
3
8
( x  5)( x  3)
Example 2: Factor x²+8x+12
•
12
6
2
8
( x  6)( x  2)
Example 3: Factor x²+13xy +36y²
36
9
4
13
( x  9 y)( x  4 y)
Example 4: Factor a²+5ab+6b²
6
2
3
5
(a  3b)(a  2b)
Signs
• When a + is in the back (or in front of the last
term), use the sign of the middle term for
both binomials
Ex : x²+9x +14 = (x +7) (x+2)
Ex x² -9x +14 = (x-7)(x-2)
Example 5: Factor y² -9y +20
-5
20
-4
-9
( y  5)( y  4)
Example 6: Factor x  8x  7
4
7
7
1
8
( x 7)( x 1)
2
2
2
Example 7: Factor m² -15m +56
56
-8
-7
-15
(m  8)(m  7)
Example 8: Factor x²-7x +10
10
-5
-2
-7
( x  5)( x  2)
Homework
• Worksheet