Question

What is 2t^3+8t^2-24t in factor form

Answer 1

2t (t-2) (t+6)

Explanation:

Answer 2

`2t^3+8t^2-24t=0\\2t(t^2+4t-12)=0\\2t=0\ \vee\ t^2+4t-12=0`


`t^2+4t-12=0\\a=1\ ;\ b=4\ ;\ c=-12\\\Delta=b^2-4ac\\\Delta=4^2-4\cdot1\cdot(-12)=16+48=64\\\sqrt\Delta=√(64)`


`t_1=(-b-\sqrt\Delta)/(2a)\ \vee\ t_2=(-b+\sqrt\Delta)/(2a)\\t_1=(-4-8)/(2\cdot1)\ \vee\ t_2=(-4+8)/(2\cdot1)\\t_1=(-12)/(2)\ \vee\ t_2=\frac42\\t_1=-6\ \vee\ t_2=2`


`2t(t^2+4t-12)=0\\2t(t+6)(t-2)=0`