Find the GCF of Each Expression. Then Factor the Expression

Name

Class

Date

Factoring Quadratic Expressions

4-4

Practice

Form K

Factor each expression.

1. x2 + 4x - 5 2. x2 + 13x + 42 3. -x2 - x + 12

4. x2 - 8x + 16 5. -x2 + 16x - 55 6. x2 + 2x - 48

7. -y2 + 17y - 72 8. x2 + 7x + 12 9. x2 - 8x + 12

Find the GCF of each expression. Then factor the expression.

10. 3x2 + 15x + 12 11. -9y2 + 6y 12. 6x2 + 12x - 48

13. -3x2 - 3x + 60 14. 2x2 - 10x 15. 7x2 - 14x - 56

16. 10x2 + 100x 17. 9x2 - 36x + 27 18. –5xy2 - 30xy - 25x

19. Writing When you factor a quadratic expression, explain what it means when c < 0 and b > 0.

20. Error Analysis You factored -x2 + 10x - 24 as -(x - 6)(x - 4). Your friend factored it as (x + 12)(x - 2). Which of you is correct? What mistake was made?

21. Multiple Choice What is the factored form of –14a2 + 42ab?

a(-14a + 42b) 7(–2a2 + 6ab)

-2a(7a - 21b) -14a(a - 3b)

22. Reasoning The area of a carpet is (x2 - 11x + 28) ft2. What are the length and the width of the carpet?

Prentice Hall Foundations Algebra 2 • Teaching Resources

Name

Class

Date

Factoring Quadratic Expressions

4-4

Practice (continued)

Form K

23. 2x2 + 7x + 6 24. 3x2 - 14x - 24 25. 5x2 - 22x + 21

26. 4x2 + 18x + 8 27. 2x2 - 8x + 6 28. 6x2 + 13x - 28

29. 4x2 - 4x + 1 30. x2 + 6x + 9 31. 4x2 - 16

32. 9x2 - 4 33. 16x2 - 40x + 25 34. x2 - 25

35. 9x2 - 36x + 36 36. 25x2 - 9 37. 4x2 + 24x + 36

38. Error Analysis Which of the following examples is factored correctly? Explain.

Example 1 Example 2

4x2 - 49 4x2 - 49

(2x)2 - 72 (2x)2 - 72

(2x - 7)(2x + 7) (2x - 7)(2x - 7)

39. You can represent the area of a square tabletop with the expression
16x2 + 24x + 9. What is the side length of the tabletop in terms of x?

Prentice Hall Foundations Algebra 2 • Teaching Resources