Factor ReviewAlgebra B

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

Summary

Factor out the GCF if it is not one

Then, look at the remaining factor.

If it is Linear, you are done factoring.

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

Factoring the difference of squares

Factoring quadratic expressions a=1

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 quadratic expressions a not 1

Is it

Cubic or a

higher degree

If it is a:

4-Term Polynomial

Try to factor by grouping.

yes

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)