Question

Help please? I need to solve by factoring.

Answer 1

Sure I'll help.

Explanation:

In order to factor the equation, we have to arrange the equation so it is all multiplication (essentially).

`2x^4 + 12x^3 + 16x^2 = 0`

First let's factor out the `2x^2`.

`2x^2(x^2+6x+8)=0`

Now, we are left with a simple trinomial in the brackets. Factor it normally.

`2x^2(x^2 + 4x+2x+8)=0`

`2x^2(x[x+4]+2[x+4])=0`

`2x^2(x+2)(x+4)=0`

Now that we have fully factored the equation, we can use this to find the solutions.

The solutions are points on the graph when `y=0`. To get this, `x` needs to equal to something that makes the entire equation `0`.

Let's start with `2x`. To get `0`, anything multiplied by `0` equals `0`. Therefore, `x=0`. That's one solution.

Next is `x+2`. Well, to get `0` here, `x` has to be `-2`, becasue `-2+2=0`. That's the second solution.

Finally, `x+4`. The same thing as before also applies here, except `x=-4`.

Therefore, the solutions to the function are `x=0, -2, -4`.

We can double check this by graphing the the function.

graph{2x^4 + 12x^3 + 16x^2 [-22.8, 22.82, -11.4, 11.4]}

Hope this helps :)