Factoring trinomials, HELP!

I understand how to factor normal trinomials like: x^2 + 9x + 20. I can do that no problem. What I do not understand is what to do with one like: y^4 + 17y^2 + 16. I'm sure it can be done... but HOW? Can anyone explain please?

Thanks

1) As you are well aware for factoring trinomials like, ax² + bx + c, factoring the other trinomial should not have any difficulty.

2) Just take y² = x; so, y^4 = (y²)² = x²

Hence, y^4 + 17y² + 16 = x² + 17x + 16 = (x + 16)(x + 1) [The steps here not explained, since you are aware of factoring this]

Substituting back x with y², the final answer is: (y² + 16)(y² + 1)

You do the same as the other one. When yu have whole numbers infront of the first number, you multiply the first and last numbers. So if the problem was 5y^4 + 15y^2 + 10 you would multiply 5 x 10 , then yu make the little chart thing x | + and plug the product from the first and last number. So id look like

x | +
50 | 15

Nd then do it like normal...

Sorry if this is confusing im a bad teacher

The easy way to doing this is, well...

Substituting.

Let's say y^2 = x. Does that make it easier?

Now its x^2 + 17x + 16.

Which I'm sure you'll understand when I say,

(x + 16)(x + 1)

Now substitute the y^2 back in...

(y^2 + 16)(y^2 + 1)

When you normally factor it, it is something like (x+2)(x-3) but instead for that one just square the variable. Because you're splitting it

y^4 + 17y² + 16

- first terms are factors of y^4.....y² and y²
- second terms multiply to get 16 and add to get 17......16 and 1

= (y² + 16)(y² + 1)

http://www.algebrahouse.com

(y^2+16)(y^2+1)