Algebra: Factoring.?

Question

I'm having some problems with factoring along with trinomials. I've gotten some weird answers for the problems below and Im hoping someone can help out cause I know im doing something wrong. ^ = Exponent.

1) Lance bicycles 37 km/h with no wind. Against the wind he bikes 75km in the same time it takes to bike 110km. What is the speed of the wind?

2) Factor: 12m^2 + 19m + 5

3) Factor: 242a^2 - 2b^2

4) Solve: 3x^3 + 4x = -8x^2

5) Solve: 9x^2 + 3x = 0

6) Factor: -x^5 + 2x^3 + x - 1

7) Factor: 4y^4x + 14yx^2 + 10y^2x^2 - 8xy

8) Factor: 9a^5b + 33ab^5

9) Factor: 18x^2 - 21x + 6

10) Divide: (3x^4 + 7x^2 + x + 4) / (x^2 + 1)

11) Divide: (y^2 + 15y + 10) / (y + 3)

12) Factor: 6x^2n - 6x^n - 12

Answer 1

1) Let x = speed of wind
d = rt
No wind:
110 = 37(t), so t = 110/37
Against wind:
75 = (37-x)(t), so t = 75/(37-x)
110/37 = 75/(37-x)
110(37-x) = 75(37)
4070 - 110x = 2775
-110x = -1295
x = 259/22 = 11.7727
2) Multiply 12 and 5
12(5) = 60
What factors of 60 add to 19?
15(4) = 60 and 15+4 = 19
Replace 19m with 15m + 4m
12m^2 + 15m + 4m + 5
Factor by grouping.
(12m^2 + 15m) + (4m + 5)
= 3m(4m+5) + 1(4m+5)
= (4m+5)(3m+1)
3) Factor out any common factors first.
242 and 2 are both divisible by 2
242a^2 - 2b^2
= 2(121a^2 - b^2)
121a^2 - b^2 is a difference of squares.
= 2(11a-b)(11a+b)
4) Move everything to one side and then factor out the common factor of x
3x^3 + 4x = -8x^2
3x^3 + 8x^2 + 4x = 0
x(3x^2 + 8x + 4) = 0
What factors of 3(4) = 12 add to 8?
6(2) = 12 and 6+2 = 8
3x^2 + 8x + 4 = 3x^2 + 6x + 2x +4
Factor by grouping
(3x^2 + 6x) + (2x +4)
= 3x(x+2) + 2(x+2)
= (x+2)(3x+2)
Now you have
x(x+2)(3x+2) = 0
Set each one equal to zero.
x =0 or x+2 = 0 or 3x+2 = 0
Answer: x = 0, x = -2, x = -2/3
5) 9x^2 + 3x = 0 Factor out the common factor (3x)
3x(3x+1) = 0
3x = 0 or 3x+1 = 0
x = 0 or x = -1/3
6) It is prime (doesn't factor)
7) Start by factoring out the common factor (2xy)
8) Start by factoring out the common factor (3ab)
9) Start by factoring out the common factor (3), then use method from #2
10) Use long division
11) Factor the top OR use long division.
12) First factor out the common factor of 6
6x^2n - 6x^n - 12
= 6(x^2n - x^n - 2)
What factors of -2 add to -1?
-2(1) = -2 and -2 +1 = -1
Answer: 6(x^n - 2)(x^n +1)

Answer 2

2) (6m +2/3)(2m+2.5)
4) x=0,-2/3, or -2
5) x=0 or -1/3

here is a start

Answer 3

im not doing your homework

3)2(121a^2-b^2) = 2(11a-b)(11a+b)

5) x=0

thats all you get