Post on 31-Dec-2015
transcript
Factoring expressionsFactoring an expression is the opposite of multiplying.
a(b + c) ab + ac
Multiplying
Factoring
Often:When we multiply an expression we remove the parentheses.When we factor an expression we write it with parentheses.
Factoring expressionsFactoring an expression is the opposite of multiplying.
Often:When we multiply an expression we remove the parentheses.When we factor an expression we write it with parentheses.
Factoring
(a + 1)(a + 2)
Multiplying
a2 + 3a + 2
Then, look at the remaining factor.
yes
Is it Quadratic?
Difference of Squares
a2 – b2 = (a-b)(a+b)
Trinomial where a = 1
Find factors of c that add to b.
Trinomial where a 1
Find factors of ac that add to b. Split the
middle term and then factor by grouping.
If it is a:
yes
Trinomial
Calculate the discriminant
b2 – 4ac.
Is it square?
yesno
Can’t be factored
more
Remember: First factor out GCF if there is one
Remember: Multiply to last term add to middle.
ax2+bx+c=( + )( + )
ax2-bx+c = ( - )( - )
ax2 bx-c = ( + )( - )
If you are using split the middle, split the linear term into two linear terms
You can Guess and Check
1253 2 xx
))(( ))(3( xx
26
62
112
121
34
43
)4)(33( xx
)3)(43( xxx12
x3
x4x9
2ax cbx Or Split the Middle Term:
Steps1. Factor out GCF if there is one.2. Identify a b c 3. Multiply a c4. Find factors of (a c) that add up to b 5. Split bx into two terms6. Factor by grouping
Factoring trinomials of form:
2ax cbx
Splitting the middle term Steps1. Factor out GCF if there is one.2. Identify a b c 3. Multiply a c4. Find factors of (a c) that add up to b
5. Split bx into two terms6. Factor by grouping
No GCF
a=6 b=-5 c=-4 a c = 6(-4)=-24
Which factors of -24 add up to -5? -8 and 3
456 2 xx
456 2 xx
4386 2 xxx)43()86( 2 xxx)43(1)43(2 xxx
)43)(12( xx
Or Another way to split the middle
First term2x2
One factor (with sign and variable)
-3x
Other factor (with sign and
variable)4x
Last term-6
Factor 2x2 + x - 61.Multiply a and c together.
2∙(-6) = -122.Find factors of ac that add up to b.
-3 and 43.Fill in a box as shown:
Factor 2x2 + x – 6
4. Factor out the common factor from the top row and place it beside the box next to the first term.
5. Factor out the common factor from the bottom row and place it beside the box next to the “other factor.”
6. Factor out the common factor from the left column and place it on top of the box above the first term.
7. Factor out the common factor from the right column and place it on top of the box above the “one factor.”
8. Put together your answer.
First term2x2
One factor (with sign and variable)
-3x
Other factor (with sign and
variable)4x
Last term-6
x
-32x
+2
(x+2)(2x-3)
Factoring by grouping
Factor a3 + a2 + 4a + 4
Two terms share a common factor of a2 and the remaining two terms share a common factor of 4.
a3 + a2 + 4a + 4 = a3 + a2 + 4a + 4
= a2(a + 1) + 4(a + 1)
a2(a + 1) and + 4(a + 1) share a common factor of (a + 1) so we can write this as
(a + 1)(a2 + 4)