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Factor Review

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

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Factor Review

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  1. Factor Review Algebra B

  2. Multiplying a(b + c) ab + ac Factoring Factoring expressions 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.

  3. a2 + 3a + 2 Factoring Factoring expressions Factoring an expression is the opposite of multiplying. Multiplying (a + 1)(a + 2) Often: When we multiply an expression we remove the parentheses. When we factor an expression we write it with parentheses.

  4. Summary

  5. Factor out the GCF if it is not one

  6. Then, look at the remaining factor. • If it is Linear, you are done factoring.

  7. Then, look at the remaining factor. Difference of Squares a2 – b2 = (a-b)(a+b) Is it Quadratic? If it is a: yes Trinomial Calculate the discriminant b2 – 4ac. Is it square? yes Trinomial where a = 1 Find factors of c that add to b. yes no Trinomial where a  1 Find factors of ac that add to b. Split the middle term and then factor by grouping. Can’t be factored more

  8. Factoring the difference of squares

  9. Factoring quadratic expressions a=1

  10. Remember: • First factor out GCF if there is one • Remember: Multiply to last term add to middle. • ax2+bx+c=( + )( + )ax2-bx+c = ( - )( - )ax2bx-c = ( + )( - ) • If you are using split the middle, split the linear term into two linear terms

  11. You can Guess and Check

  12. Or Split the Middle Term: Steps Factor out GCF if there is one. Identify abc Multiply ac Find factors of (ac) that add up to b Split bx into two terms Factor by grouping

  13. Factoring trinomials of form: Splitting the middle term Steps Factor out GCF if there is one. Identify abc Multiply ac Find factors of (ac) that add up to b Split bx into two terms Factor by grouping No GCF a=6b=-5c=-4 ac = 6(-4)=-24 -8 and 3 Which factors of -24 add up to -5?

  14. Or Another way to split the middle • Factor 2x2 + x - 6 • Multiply a and c together. 2∙(-6) = -12 • Find factors of ac that add up to b. -3 and 4 • Fill in a box as shown:

  15. 2x -3 • Factor 2x2 + x – 6 • Factor out the common factor from the top row and place it beside the box next to the first term. • Factor out the common factor from the bottom row and place it beside the box next to the “other factor.” • Factor out the common factor from the left column and place it on top of the box above the first term. • Factor out the common factor from the right column and place it on top of the box above the “one factor.” • Put together your answer. x +2 (x+2)(2x-3)

  16. Factoring quadratic expressions a not 1

  17. Is it Cubic or a higher degree 4-Term Polynomial Try to factor by grouping. If it is a: yes

  18. Factoring by grouping Factor a3+ a2+ 4a + 4 Two terms share a common factor of a2and 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)

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