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, +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.
