 # Algebra B. Factoring an expression is the opposite of multiplying. a ( b + c ) ab + ac Multiplying Factoring Often: When we multiply an expression we.

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Algebra B

Factoring 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 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 a 2 + 3 a + 2

Factor out the GCF if it is not one

If it is Linear, you are done factoring.

yes Is it Quadratic? Difference of Squares a 2 – b 2 = (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 b 2 – 4ac. Is it square? yes no Can’t be factored more

Factoring the difference of squares

 First factor out GCF if there is one  Remember: Multiply to last term add to middle.  ax 2 +bx+c=( + )( + ) ax 2 -bx+c = ( - )( - ) ax 2 bx-c = ( + )( - )  If you are using split the middle, split the linear term into two linear terms

Or Split the Middle Term: Steps 1.Factor out GCF if there is one. 2.Identify a b c 3.Multiply a c 4.Find factors of (a c) that add up to b 5.Split bx into two terms 6.Factor by grouping

Factoring trinomials of form: Splitting the middle term Steps 1.Factor out GCF if there is one. 2.Identify a b c 3.Multiply a c 4.Find factors of (a c) that add up to b 5.Split bx into two terms 6.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

First term 2x 2 One factor (with sign and variable) -3x Other factor (with sign and variable) 4x Last term -6 Factor 2x 2 + x - 6 1.Multiply a and c together. 2∙(-6) = -12 2.Find factors of ac that add up to b. -3 and 4 3.Fill in a box as shown:

Factor 2x 2 + 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 term 2x 2 One factor (with sign and variable) -3x Other factor (with sign and variable) 4x Last term -6 x -3 2x +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. yesyes

Factoring by grouping Factor a 3 + a 2 + 4a + 4 Two terms share a common factor of a 2 and the remaining two terms share a common factor of 4. a 3 + a 2 + 4a + 4 = a 3 + a 2 + 4 a + 4 = a 2 ( a + 1) + 4 ( a + 1) a 2 ( a + 1) and + 4 ( a + 1) share a common factor of ( a + 1) so we can write this as ( a + 1)( a 2 + 4 )

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