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# Algebra: Factorzation & Principle of Zero Products

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128. Factor completely Remember to look first for a common factor. Check by multiplying. If a polynomial is prime, state this.
− x3 + x2 + 42x
28. Factor completely. Remember to look first for a common factor and to check by multiplying. If a polynomial is prime, state this.
25x2 + 10x + 1
8. Solve using the principle of zero products.
(5t − 8)(t −1) = 0
1. Complete the factorization.

8x6 = 4x2( )

2. Factor out the largest common factor.

y8 - 16y5

3. Factor out the largest common factor.

5x(3x - 5) + 2(3x - 5)

4. Factor by grouping, if possible. Show all work necessary.

x3 + 3x2 + 2x + 6

5. Factor completely. Show all work necessary.

x2 - 5x - 24

6. Factor completely. Show all work necessary.

3x2 - 27x + 60

7. Factor completely. Show all work necessary.

7x2 + 58x - 45

8. Factor completely. Show all work necessary.

9x2 - 121

9. Factor completely. Show all work necessary.

x2 - 10x + 25

10. Solve using the principle of zero products.

(y + 17)(y + 5)(y - 3) = 0

11. Solve by factoring and using the principle of zero products. Show all work necessary.

5x2 - 66 = 4x2 + 5x

12. Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.

The product of two consecutive positive integers is 109 more than their sum. Find the integers

13. Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.

A 20-ft. ladder is leaning against a building. If the distance from the bottom of the ladder to the base of the building is 4 ft. less than the height on the wall where the ladder is resting, what is the length of this height on the wall?

1. Factor out the largest common factor.
6x9z5 - 18x6z3 + 4x5z4 - 22x7z6

2. Factor by grouping, if possible. Show all work necessary.
4x2 - 3x + 20x - 15

3. Factor completely.
x2 + 11x - 26

4. Factor completely.
-x5 - 2x4 + 99x3

5. Factor completely.
u2 - 6uv - 27v2

6. Factor completely.
24x3 + 14x2 - 20x

7. Factor completely.
75x2 - 3
8. Factor completely.
t5 - 81t

9. Factor completely.

4a2 + 16a + 16

10. Factor completely.
4x2 - 20xy + 25y2

11. Solve by factoring and using the principle of zero products.
a2 - 19a = 0

12. Solve by factoring and using the principle of zero products.
(x - 9)(x - 3) = -8

13. Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
A rectangular room is 7 feet longer than it is wide. If the area of the room is 228 square feet, find the length and the width.

14. Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
A cement walk of uniform width is built around a 20 foot by 40 foot rectangular pool and the area of the walk is 700 square feet. How wide will the walk be

15. Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution.
If an object is propelled upward from a height of 96 feet at an initial velocity of 80 feet per second, then its height h after t seconds is given by the equation h = - 16t2 + 80t + 96. After how many seconds does the object hit the ground?