Definition:Reducible Polynomial/Mistake

Source Work

1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.)

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.):

reducible polynomial

Mistake

A *polynomial is reducible over a *field $F$ if it can be factored into two polynomials having coefficients in $F$.

Correction

It needs to be specified either that:

the $2$ polynomials must be of strictly lesser degree than their product

or that:

neither of the $2$ polynomials may be a constant polynomial, that is, of degree $0$.

Otherwise, for example, the polynomial over $\R$:

$2 x^2 + 2$

would be reducible as:

$\paren 2 \paren {x^2 + 1}$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reducible polynomial
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reducible polynomial