Many times a component of a term or terms in a ** polynomial **
is left **unwritten**. Students often make the

mistake of using the missing component as the wrong value , as a 0 instead of a 1
for example. I am

going to list some of these here and then demonstrate their misuse with some
examples.

**Unwritten Components**

Therefore, **X **actually means, and could be written
as, **+1X**^{1}.

**Examples of Misuse:**

When using the Rules of Exponents to multiply ** polynomials **, we must add
** exponents **. Misusing an

**unwritten** 1 as a 0 will cause an incorrect answer.

X * X^{2} * X^{3} is X^{6} not X^{5} because the
** exponents ** to add are **1**, 2, and 3.

When adding and subtracting ** polynomials **, we must add and subtract the
** coefficients **. Misusing an

**unwritten** 1 as a 0 will cause an incorrect answer.

5X + 3X + X + 2X is 11X not 10X because the ** coefficients ** to add are 5, 3,
**1**, and
2.

Cases of misusing an** unwritten** positive ** sign ** would be far less common, but it
seemed to make sense to

include in this discussion. It is absolutely necessary to write the **sign **if it
is negative, it is OK to write

the sign if it is positive, and if the **sign** is **unwritten **, then the
**sign** is
assumed to be positive. It is also

necessary to be careful not to omit a positive or negative **sign** that is an
addition or subtraction **sign.** The

** operation signs ** should never be **unwritten**.

X(Y – 2) is XY – 2Y not XY 2Y because the ** operation signs ** are always
**written.**