You may want to review factoring polynomials first.

It's helpful to be able to recognize when a polynomial is a square. There are three conditions to check:

• The x2 term must be a square.
• The constant (or y2, if there's a y too) term must also be a square.
• If you take the square roots of those two terms and multiply them together, you get the other term.

For example, consider 4x2 + 6x + 9. We see that 4x2 is the square of 2x and 9 is the square of 3. Now, we multiply 2x by 3 and get 6x, the same as the other term, so it's a square. In particular, it's the square of 2x + 3.

If the x2 term or the constant term were negative, then it wouldn't be a square. But that's not true of the other term. In fact, 4x2 − 6x + 9 is a square; it's the square of 2x − 3.

Not all the polynomials I ask you to factor in this section are actually squares. Some of them have GCDs. You need to factor them out first. There's a spot for you to write the factor that should be squared and a another spot for you to write the GCD which shouldn't be. Don't confuse the two!