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Polynomials-The Unwritten Rules

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

Component Unwritten Written
Coefficient X
Exponent X
Sign X

Therefore, X actually means, and could be written as, +1X1.

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 * X2 * X3 is X6 not X5 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.

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