Factoring Review

Factoring The process of rewriting an equation or expression as the product of its factors Example: x2 + 3x + 2 = (x + 2)(x + 1) Most common form is the quadratic form: ax2 + bx + c, a ≠ 0

Factoring (when a = 1) ax2 + bx + c = (x + ___ ) (x + ___ ) multiply to equal c and add up to equal b You can always check your answer by FOIL-ing!

Finding Factors of C Identify the value of c On your calculator, go to the y= screen Type C/X into y1 Go to the table Any whole numbers (positive, non-decimal numbers) in the y1 column are factors of c

Example

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Your Turn: Complete problems 1 – 3 on the “Factoring Practice” handout Check your answer by FOIL-ing!

1. (x + 9)(x + 2) 2. (y – 7)(y + 5) 3. (g – 6)(g + 2)

Difference of Squares When we use it: Usually in the form ax2 – c Both a and c are perfect squares (the square root of each number is a whole number)

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Your Turn: Complete problems 4 – 10 on the “Factoring Practice” handout Remember to check your answer by FOIL-ing!

4. 5. 6. 7. 8.

Factoring (when a ≠ 1): The Welsh Method Multiply c and a Rewrite the expression with the new value for c Write (ax + )(ax + ) Finish “factoring” the new expression Reduce each set of parentheses by any common factors

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Your Turn: Complete problems 11 – 20 on the “Factoring Practice” handout Don’t forget to check by FOIL-ing!

11. 12. 13. 14. 15. 16.

GCF (Greatest Common Factor) When we use it: all the terms share 1 or more factors Factoring out GCFs save us time!!! 4x2 – 196 = 0 (2x + 14)(2x – 14) = 0

GCF (Greatest Common Factor) Steps: Identify any common factor(s) (including the GCF) Factor out the common factor(s) Factor the remaining expression if possible

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Your Turn: Complete problems 17 – 27 on “Factoring Practice” handout

17. 18. 19. 20. 21. 22.

23. 24. 25. 26. 27.

Warm-up (2 m) 20x6y7 + 12xy3 + 28x7y2 6x2 + 19x - 11

GCFs and The Welsh Method Make sure you factor out any GCFs or the Welsh Method doesn’t work!!!

Your Turn: Complete problems 28 – 33 on the “Factoring Practice” handout using the GCF and the Welsh Method

28. 29. 30. 31. 32. 33.

Picking the Correct Method 34. x2 + 10x + 16

Picking the Correct Method 35. 5t2 + 28t + 32

Picking the Correct Method

Your Turn: Completely factor problems 36 – 44 on the “Factoring Practice” handout. In your solution, state the method(s) you used to completely factor the expression.

37. 38. 39. 40.

41. 42. 43. 44.