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Test

Factoring Polynomials

 

~Circle the letter to the word that best fits the definition, worth 5 points each

 

1.  Which of the following is a perfect example of a “Perfect Square Trinomial”?

 

                        A.)       25y² + 30y + 4

                        B.)       9a² - 6a + 1

                        C.)       (7m)² - 24m + (2)²

                        D.)       none of the above

 

 

2. Which of the following is a Quadratic Equation in standard form?

           

A.)       7x - 2x² + 4 = 0

                        B.)       -2x² + 4 = 7x

                        C.)       4 + 7x = -2x²

                        D.)       none of the above

 

~Write in the letter of the example that best matches each mathematical term in the blank column by the terms, worth 2 points each

 

3.         Mathematical Terms                                     Examples

 

    ____1. Foil Method                                                 a.  (a)(b)=0 then a=0,b=0,or a & b=0

 

    ____2. Product Property of Zero                              b. solution of an equation

 

    ____3. Factoring by Groups                         c. integers divisible by two

 

    ____4. Cubic Equation                                             d. ax²+bx+c=0

 

    ____5. Roots                                                           e. using a common monomial

 

                                                                                    f. third degree equation

                                                                                   

                                                                                    g. first, outer, inner, last

 

 

 

 

 

 

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~Solve Each Equation; Show All Work, Worth 4 points each

 

6. y² +15y+26=0

 

 

 

 

7. 16m=12-3m²

 

 

 

 

 

8. 2x²+3x²-35x=0

 

 

 

 

 

9. p+56=p²

 

 

 

 

 

10. 28=y+2y²

 

 

 

 

 

 

 

~Multiply the following, Show All Work, Worth 4 points each

 

11. (5x-2)(5x+2)

 

 

 

 

12. (3a+4c)(5a-2c)

 

 

 

 

13. (3x+2)(x²-5x+4)

~Factor each Polynomial completely; Show All Work, Worth 4 points each

 

 

14. a²-7a+10

 

 

 

 

 

 

15. 2x²-xy-15y²

 

 

 

 

 

 

16. 25k²-49b²

 

 

 

 

 

 

17. x³y-16xy³

 

 

 

 

 

~Determine if each trinomial is a perfect square. If so factor it. Show All Work, Worth 4 points each

 

 

18. 36b²-18b+9

 

 

 

 

 

 

19. 16x²-24xy+9y²

 

 

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~Solve each problem; Show All Work, Worth 4 points each

 

20.  If 2 times a number is added to the square of the number, the result is 24.    Find the two solutions

 

 

 

 

 

21. Find three consecutive odd integers whose product is 315.

 

 

 

 

 

 

 

22. Find two consecutives even integers such that the square of the first decresed by twice the second is 20.

 

 

 

 

 

 

23. Solve 2a -68a³+450a=0

 

 

 

 

 

24. Multiply: (3x+5)(x-2)(x+3)

 

 

 

 

 

 

25. Factor completely: x²a²-4a²y²-9x²+36y²