Expert: Richard J. Raridon - 6/13/2009

Question
1. Factor the polynomial:
121x^2 - 1  


2. Factor the polynomial:
16x^2 + 40xy + 25y^2

3. Factor the polynomial:
8p^3 + 1

4. Factor the polynomial:
u(v - 1) + 2(v - 1)  

5. Factor the polynomial:
z^2 + 3z - 4


6. Factor the polynomial:

u^2 - 10u + 9

7. Factor the polynomial:
h^2 - 10h + 24

8. Factor the polynomial:
p^2 + 2pq - 24q^2

9. Factor the polynomial:
3x^2 - 8x + 5

10. Factor the polynomial:
4y^2 - 17y + 15  


11. Factor the polynomial:
4r^2 + 16rs + 10s^2

12. Factor the polynomial:
81uv^3 + 3u^4  


13. Factor the polynomial:
z^4 - 10z^2 + 9


14. Solve:
z^2(2z - 1) = 0  


15. Solve:
y^3 + 6y^2  =  27y  

16. Solve:
10t^2 - 9t = 1


17. Solve:
(u + 3)(u - 3) = 8u  

Answer
Your clue on 1 and 2 is the presence of squares
1. (11x+1)(11x-1)
2. (4x+5y)^2
3. (2p+1)(4p^2-2p+1)
4. (u+2)(v-1)
ones like 5 always have to be in the form (z+a)(z+b) where ab = c.
in this case ab = -4 so a and b have to be 2 & 2 or 4 & 1.  not many options to try.  same on 6 & 7.
5. (z+4)(z-1)
6. (u-9)(u-1)
7. (h-4)(h-6)
8. (p+6q)(p-4q)
9. (3x-5)(x-1)
10. (4y-5)(y-3)
11. cannot factor
12. 3u(3v+u)(9v^2-3uv+u^2)
13. (z+1)(z-1)(z+3)(z-3)
14. z = 0,1/2
15. y(y-3)(y+9)
16. t = 1, -1/10
17. u = -1, 9
I hope you're learning something