What is the fully factored form of 4x^{3}+16x^{2}-48x?
4x(x-2)(x+6)
(4x^{2}-8x)(x+6)
(4x^{2}+24x)(x-2)
4(x^{2}-8x)(x+6)
Emmy factors the quadratic trinomial -10q^{2}+13q+3 by grouping. Match each of her steps with its explanation.
(-10q^{2}+15q)+(-2q+3) = (15q-10q^{2})+(3-2q)
Decomposition of a Sum: 13q=15q+-2q
(15q-10q^{2})+(3-2q) = 5q(3-2q)+(3-2q)
Associativity of Addition: a+b+c=(a+b)+c=a+(b+c)
5q(3-2q)+1(3-2q)=(5q+1)(3-2q)
Commutativity of Addition: a+b = b+a
-10q^{2}+(13q)+3 = -10q^{2}+(15q+-2q)+3
Distributive Law (of multiplication over addition): a(b+c)=ab+ac
-10q^{2}+(15q+-2q)+3= (-10q^{2}+15q)+(-2q+3)
Multiplicative Identity: 1\cdot a=a
5q(3-2q)+(3-2q)=5q(3-2q)+1(3-2q)
Distributive Law (of multiplication over addition): a(b+c)=ab+ac
The area of a circle, A, is given by A=\pi r^{2}, where r is the radius of the circle and \pi is an irrational constant approximately equal to 3.141593.
If the area of a circular trampoline is equal to 4\pi x^{2}+16\pi x+16\pi \textrm{ cm}^{2}, then which of the following could be possible lengths of the circle's radius?