2. Factoring Polynomials
1032
−− xx
This process is basically the REVERSE
of the distributive property.
=−+ )5)(2( xx
distributive property

3. =−− 1032
xx
In factoring you start with a polynomial
(2 or more terms) and you want to rewrite it
as a product (or as a single term)
Factoring Polynomials
)5)(2( −+ xx
Three terms
One term

4. What is a perfect square?

6. 652
++ xx We need to find factors of 6
….that add up to 5

7. Factoring Trinomials, continued...
652
++ xx 2 x 3 = 6
2 + 3 = 5
Use the numbers 2 and 3 to factor the trinomial…
Write the parenthesis, with
An “x” in front of each.
( )3)2( ++ xxWrite in the two numbers
we found above.
( )xx )(

8. 652
++ xx
You can check your work by multiplying back
to get the original answer
( )3)2( ++ xx
( )3)2( ++= xx
=+++= 6232
xxx
652
++= xx
So we factored the trinomial…
Factoring Trinomials, continued...

9. Factoring Trinomials
61
65
67
2
2
2
−+
−−
++
xx
xx
xx
Find factors of – 6 that add up to –5
Find factors of 6 that add up to 7
Find factors of – 6 that add up to 1
6 and 1
– 6 and 1
3 and –2

10. 61
65
67
2
2
2
−+
−−
++
xx
xx
xx
factors of 6 that add up to 7: 6 and 1
( )1)6( ++ xx
factors of – 6 that add up to – 5: – 6 and 1
factors of – 6 that add up to 1: 3 and – 2
( )1)6( +− xx
( )2)3( −+ xx
Factoring Trinomials

11. Factoring Trinomials
The hard case – “Box Method”
62 2
−+ xx
Note: The coefficient of x2
is different from 1. In this case it is 2
62 2
−+ xx
First: Multiply 2 and –6: 2 (– 6) = – 12
1
Next: Find factors of – 12 that add up to 1
– 3 and 4

12. Factoring Trinomials
The hard case – “Box Method”
62 2
−+ xx
1. Draw a 2 by 2 grid.
2. Write the first term in the upper left-hand corner
3. Write the last term in the lower right-hand corner.
2
2x
6−

13. Factoring Trinomials
The hard case – “Box Method”
62 2
−+ xx – 3 x 4 = – 12
– 3 + 4 = 1
1. Take the two numbers –3 and 4, and put them, complete
with signs and variables, in the diagonal corners, like this:
2
2x
6−
It does not matter which
way you do the diagonal
entries!
Find factors of – 12 that add up to 1
–3 x
4x

14. The hard case – “Box Method”
1. Then factor like this:
2
2x
6−
x3−
x4
Factor Top Row Factor Bottom Row
2
2
2x
6−
x3−
x4
x
From Left Column From Right Column
2
2x
6−
x3−
x42
x
x2
2
2x
6−
x3−
x4
x2
2
x
3−
x

15. The hard case – “Box Method”
2
2x
6−
x3−
x4
x2
2
x
3−
)32)(2(62 2
−+=−+ xxxx
Note: The signs for the bottom row
entry and the right column entry
come from the closest term that you
are factoring from.
DO NOT FORGET THE SIGNS!!
++
Now that we have factored our box we can read off
our answer:

16. The hard case – “Box Method”
2
4x
12
x16−
x3−
x
3
x4
4
=+− 12194 2
xx
Finally, you can check your work by multiplying
back to get the original answer.
Look for factors of 48 that add up to –19 – 16 and – 3
)4)(34(12194 2
−−=+− xxxx

17. Use “Box” method to factor
the following trinomials.
1. 2x2
+ 7x + 3
2. 4x2
– 8x – 21
3. 2x2
– x – 6

18. Factoring the Difference of Two
Squares
The difference of two bases being squared,
factors as the product of the sum and difference
of the bases that are being squared.
a2
– b2
= (a + b)(a – b)FORMULA:
(a + b)(a – b) = a2
– ab + ab – b2
= a2
– b2

19. Factoring the difference of two squares
Factor x2
– 4y2
Factor 16r2
– 25
(x)2
(2y)
2
(x – 2y)(x + 2y)
Now you can check the results…
(4r)
2
(5)
2
Difference
of two squares
Difference
Of two squares
(4r – 5)(4r + 5)
a2
– b2
= (a + b)(a – b)

20. The information was taken from the
following people on slideshare:
Estela, Sep 22 2013. Factorising
quadratic expressions 1http://www.slideshare.net/estelav/factorising-quadratic-expressions-1
Julia Li,http://www.slideshare.net/jagheterjuliali/ch-06-10762231
Majapamaya, Nov 13, 2013. 05 perfect
square, difference of two squareshttp://www.slideshare.net/majapamaya/05-perfect-square-difference-of-two-squares
Swart J.E, Oct 28 2013. Factoring and
Box Methodhttp://www.slideshare.net/swartzje/factoring-and-box-method