Solving Polynomial Equations, in Depth

Let's work through an example to see what one of these word problems could look like.

At first, this looks a little barf-worthy, right? That's a lot of words. The trick with all word problems is to translate the words into mathematical expressions.

Let's start here: "2 consecutive odd integers"

So, our two integers are: $x$ and $x+2$.

To verify this, think of any odd number. Let's just use 3. The next (consecutive) odd integer is 5. We can see that 5 is 2 greater than 3, so it appears that our choice to represent the two integers as $x$ and $x+2$ is correct.

The next part of the word problem says "the product of two consecutive odd integers."

So, the product of these two integers is: $x\left(x+2\right)$.

The rest of the word problem says that this product $\left(x\cdot\left(x+2\right)\right)$ "**is equal to ** negative one minus the sum of the two integers."

Let's set that up.

So, we've translated the word problem into this equation:

We can then simplify this equation like we would with any other.

Now, we can factor our quadratic equation to solve for x.