# Solve #2x^3 + x^2 = -4 - 8x#?

##### 1 Answer

graph{2x^3 + x^2 + 8x + 4 [-11.06, 11.44, -4.63, 7.09]}

#### Explanation:

First thing you always want to do when solving polynomial equations is set them equal to zero. So:

Now, we're going to use a method of solving called **grouping.** We're going to split the left hand side of our equation into two groups of 2 terms each, and then try to factor out some common term out of each group.

I see that I can factor out a

Since I have a

Now that I have a product of factors, I can invoke my zero product property, and know that for this equation to be true, one of those factors must equal zero.

...but wait, how can we have a negative number under our square root? The answer is we cannot! That is, we cannot have a negative number inside a square root *and expect a real number as an answer*. So your only *real* solution to this equation would be

However, you should only ever include this in your answer if it imaginary solutions are specifically asked for.

A handy way to check your answer right after is to graph it. Let's see how that turns out:

graph{2x^3 + x^2 + 8x + 4 [-11.06, 11.44, -4.63, 7.09]}

You'll see that our graph does in fact intersect the x-axis at

Here's a great video by patrickJMT if you want to learn more about the process of grouping;

Hope that helps :)