MATH 114N Week 3 Test 1 Review Guide

(MATH 114N Week 3 Test 1 Review Guide)

To help with the Unit 1 Review (quite difficult for students), the following explanation of each problem is useful on the Review. Please note that the questions on your Review may have different numbers, but the concept is the same as the following. Remember, the “^” indicates an exponent. We hope this helps!

– To begin, remember that the greatest common factor (GCF) may consist of a number and/or a
– The GCF of the coefficients (numbers) is the largest number that divides into each
– The GCF of the variable(s) is the variable with the smallest exponent that appears on a variable that is in every

1. Question: Find the greatest common factor (GCF) of: 16x and 36
2. Question: Complete the factoring: 5y + 30 = 5( )
3. Question: 10t^2 + 5t
4. Question: Factor by grouping: x^3 + 4x^2 + 9x + 36
5. Question: What polynomial can be factored as (a+8)(a+5)?
6. Question: Factor the trinomial: r^2 +5r + 4
7. Question: Factor the trinomial: w^2+5w + 66
8. Question: Factor the trinomial: v^2 +9vz + 20z^2
9. Question: Complete the factoring: 2x^3 + 8x^2 + 6x
10. Question: Note that the middle term has already been split: 27r^2 – 24r + 36r – 32
11. Question: The middle term of the trinomial has been Now factor by grouping:
    15r^2 + 26rs + 8s^2 = 15r^2 + 20rs + 6rs + 8s^2
12. Question: Factor the trinomial by grouping: 15m^2 – 17m – 4
13. Question: Complete the factoring: 2v^2 + 10v – 12 = 2( )( )
14. Question: Complete the factoring: 15s^3 – 48s^2 + 9s = 3s (        ) = 3s(             )(          )
15. Question: Which of the following are differences of squares?
    b^2 – 25 ; y^2 + 36 ; 5x^2 – 4 ; 25^2 – 1
    
16. Question: Factor completely: c^2 + 9
17. Question: Factor completely: 49r^2 – 16d^2
18. Question: Factor the special product: 64v^2 – 144v + 81
19. Question: Factor: 16x^2 – 56xy + 49y^2
20. Question: Solve using the zero-factor property: (2a + 5)(a + 4) = 0
21. Question: Solve:  t^2 – 19t + 18 = 0
22. Question: Solve:  t^2 – 4 = 0
23. Question: The area of a parallelogram is given by the formula A = (NOTE: Please see the picture given in the problem for additional help with this.) The area of the parallelogram with height (x+1) and base (2x + 1) is 45 sq. units. Find its base and height
24. Question: The product of two consecutive positive integers is 5 more than their Find the integers.
25. Question: Rosa works due north of Her husband Ben works due east. They leave for work at the same time. By the time Rosa is 3 miles from home, the distance between them is one mile more than Ben’s distance from home. How far from home is Ben?
26. Question: If an object is projected upward with an initial velocity of 128 ft per sec, its height “h” after “t” seconds is h = -16t^2 + Find the height of the object after 5 seconds.