Factoring Review AMT

Step1. Look for GCF and factor it out to the front 1. 7x + 49 2. 8ax – 56a 3. t2h + 3t 4. x + x2y + x3y3 5. 4a 2b2 + 16ab + 12 a

Factoring by grouping (only do this when there are 4 terms without a GCF) 1. Group the first two terms and the last two terms 2. Pull out a GCF for each group 3. The ( ) should be the same 4. Final answer is the ( ) that are the same and the GCF’s in the second ( )

Examples 6-8 6. x2 + 3x + x + 3 7. 2x2 + 2x + 3x + 3

Solving 1. Get everything on one side so the equation is set = 0 then factor just like you normally would. 2. Set each factor equal to 0 and solve for the variable

Examples 9-11 9. x(x – 8) = 0 10. x2 – 5x = 0 11. 3x2 = 6x

Trinomials 1. Factors of the last term that + or – to give you the middle term 2. Last term + and middle term - ( - )( - ) Last term + and middle term + ( + )( + ) Last term – means ( + ) ( - ) Larger factor goes with the sign of the middle term

Examples 12-24 12. t2 + 8t + 12 13. p2 + 9p + 20 14. n2 + 3n – 18 15. y2 – 5y - 6

16. x2 + 4x -12 17. w2 – w – 6 18. x2 – 8x + 15 19. t2 – 15t + 56

20. x2 – 6x + 8 = 0 21. m2 + 5m + 6 = 0 22. y2 – 2y -24 = 0 23. h2 + 2h = 35 24. n2 – 36 = 5n

More Trinomials “Beef” it up and “Cut” the fat Same rules as earlier but now we want factors of the product of the first and last terms. Cut out the GCF at the end

Examples 25-35 25. 2x2 + 5x + 2 26. 2x2 + 9x – 9 27. 2x2 + x – 1

30. 3a 2 + 30a + 63 31. 2x2 + 7x + 3 = 0 32. 3x2 – 7x + 2 = 0

33. 6x2 + 8x + 2 = 0 34. 9x2 + 18x – 12 = 6x 35. 10x2 – 15x = 8x – 12

Differences of Squares Factor into ( + ) ( - ) Take the square root of each term

Examples 36-42 36. 1 – 49d2 37. t2 – 81u2 38. 64x2 – 9y2 39. 20x2 – 5y2 40. 16x2 – 9 = 0 41. 36b2 – 49 = 0 42. n2 – 9 = 0