**Try the easy way first.**

If evaluating the polynomial, whatever it is, at *x* = 4 and then adding 2 gives 2, that must mean that the value of the polynomial at that point is 0. Lucky for you.

If the value of *p*(4) is 0, that means 4 must be a root of the polynomial, or a zero. And *that* means that (*x* – 4) is a factor of the polynomial. It has to be.

In other words, this polynomial could do all kinds of crazy things, but at *x* = 4, it has to hit the *x* axis, giving a *y* value of 0. Maybe the polynomial looks like this:

Maybe it looks like this:

**But whatever it looks like, wherever it wanders, if it crosses the ***x* axis at 4, one thing you know for sure is that (*x* – 4) is one of the factors.

If you think about this question for a little while, pondering the beauty and perfection of algebra and mathematics in general, you will quickly discover that the *only* way you can answer a question like this is if you know a zero of the polynomial.

That means, whenever this topic is tested in algebra 2, the question writer has to give you some way of figuring out what the zero or zeroes are for the polynomial. That’s the only way you can determine what one of the factors is for an unknown polynomial.

Keep in mind that polynomials may be represented graphically as well as algebraically. But however the unknown polynomial is described, just remember you need to know the zeroes.

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