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8/9/2019 Factoring 4

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Name:_______________________ Class Time:________________ Due: __________

Factoring IV

Complete the table below and use it for reference in the problems that follow:

number 1 2 3 4 5 6 7 8 9 10

double

square

cube

Are each the following equivalent? (Yes / No)

252 x , 2502

+ xx , 25552

+ xxx , 25442

+ xxx

Which of the above can be factored with grouping in their current form? . any/all that apply.

Multiply with FOIL, Rewrite each below in such a way

then simplify. that it can be factored with grouping,

then factor completely.

1a. ( ) ( )4 4x x + 1b. 162 x

2a. ( ) ( )7 7a y a y+ 2b. 22 49ya

3a. ( ) ( )a b a b + 3b. 2 2a b

4a. #3b is the formula for the ____________________ of two ___________________.

The key is to figure out what is youra term and what is yourb term.

Look at the following.2 281 100y x

If22 81ya = , then =a ______________.

If 22 100xb = , then =b ______________.

4b. Now use the formula from 3b factor:22 10081 xy .

MAT121/Factoring IV/Page 1 of 4

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5a. Determine a and b and use these to help you factor: 225 9x

a = _____________, b = ______________.

2

25 9x = (___________)(_____________)

5b. If 16)3(222

+= xba , then a = _____________, and b = ______________.

Your answer below should be in the form: ))(( baba +

Now factor: ( ) 1632

+x = (___________)(___________)

5c. Now, take your answer from 5b and simplify within the parentheses.

Your answer should be in the form: ( ) )( BxAx +

5d. Expand ( ) 163 2 +x , combine like terms and simplify completely.

5e. Factor the trinomial found in 5dand compare to the answer found in 5c.

Multiply and simplify completely. Factor. (No work necessary, just write formula

6a. ( ) ( )2 2a b a ab b+ + 6b. 3 3a b+

7a. ( ) ( )2 2

a b a ab b + + 7b. 3 3a b

8. a) You now have formulas to factor the sum ordifference of two _________________.



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8b) Rewrite each formula below: (and start memorizing them now!)

Sum of two cubes formula:_______________________________________________

Difference of two cubes formula:__________________________________________

8c) Again, find the a and b first. What is youra and b for the following? Factor it.

273 +x a = _____________, b = ______________.

Find youra and b, then factor.

9. 64125 6 y a = _____________, b = ______________.

** Journal entry: Is the following factorable: 2 16x + ? Why or why not?So what can you say about factoring the sum of two squares?

Carefully factor each polynomials below. All of the types of factoring are represented here.

(You may find it necessary to use multiple methods within a single problem)

WORK THESE OUT ON YOUR SCRATCH PAPER OR WHITEBOARDS FIRST!!

10. 93025 22 ++ xyyx 11(a) 153 5416 yx

12. 8116249 22 + baba

11(b) MULTIPLY to check your answer



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13.(a)22 4914 yyx ++ 13 (b) MULTIPLY to check your answer

(watch your signs!)

14. 36 8xa + 15. ( )22 14 + yx

16. 482 ++ xx 17.86 xy

18. 36122 ++ xx 19. 25102 + xx

Journal Entry: What do you notice about the result of factoring #18 and 19? Look at the original

problem and determine why this works. Now make up your own polynomial that will have similarresults when factored.


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