Math a Factoring strategy

Factor.
1) 14y^3+6y^4-40y^2
=2y^2 (3y^2+7y-20)
=2y^2 (3y-5) (y+4)
2) j^4-16
=(j^2+4) (j^2-4) using a^2-b^2=(a+b)(a-b)
=(j^2+4) (j+2)(j-2)
3) 400x+400-m^2 x -m^2
=400(x+1) – m^2(x+1)
=(400-m^2)(x+1)
=(20+m)(20-m)(x+1)
4) 5s^2 t+ 5s^2 u^2+5tv +5u^2v
=5[s^2(t+u^2) + v(t+u^2)]
=5(s^2+v)(t+u^2)
5) -3j^3 -24
=-3(j^3+8)
=-3(j+2)[(j+2)^2-6j] using a^3+b^3=(a+b)^3-3ab(a+b)=(a+b)[(a+b)^2-3ab]
6) 12w^4 -36w^3 +27w^2
=3w^2(4w^2-12w+9)
=3w^2(2w-3)^2
7) 2t^3+10
=2(t^3+5)
If modify question to 2t^3+16
=2(t^3+8)
=2(t+2)[(t+2)^2-6t] see Q5
8) x^2 z+64y^2 z+16xyz
=z(x^2+16xy +64y^2)
=z(x+8y)^2
9) 121p^2+36q^2
=(11p+6q)^2-2(11p)(6q) using a^2+b^2=(a+b)^2-2ab
=(11p+6q)^2-132pq
10) 18c^3 d^2 -12c^3 d-24c^2 d
=6c^2 d(3cd-2c-4)

Solving Quadratic Equations by factoring.
1) 8x(x-6)=0
x=0 or x-6=0
x=0 or x=6
2) x^2+2x=0
x(x+2)=0
x=0 or x=-2
3) 144x^2 -25=0
(12x+5)(12x-5)=0 using a^2-b^2=(a+b)(a-b)
x=-5/12 or x=5/12
4) (4x-7)(x+1)=0
x=7/4 or x=-1
5) x^2-9=0
(x+3)(x-3)=0 using a^2-b^2=(a+b)(a-b)
x=-3 or x=3
6) a^2-7a+12=0
(a-3)(a-4)=0
a=3 or a=4
7) 2t^2+28t+98=0
2(t^2+14t+49)=0
2(t+7)^2=0
t=-7
8) 5a^2-61+1=0
5a^2-60=0
5(a^2-12)=0
5(a+sqrt 12)(a-sqrt 12) using a^2-b^2=(a+b)(a-b)
5(a+2 sqrt 3)(a- 2 sqrt 3) using sqrt 12=sqrt (2^2)3=sqrt (2^2) sqrt 3=2 sqrt 3
9) 2x-x^2=-24
x^2-2x-24=0 moving LHS to RHS
(x-6)(x+4)=0
x=6 or x=-4
10) 2p^3=2p(p+2)
2p^3=2p^2+4p
2p^3-2p^2-4p=0 moving RHS to LHS
2p(p^2-p-2)=0
2p(p-2)(p+1)=0
p=0 or p=2 or p=-1