## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 256

With these laws of addition and multiplication, the

The ring has unity: the

nor g (x) is zero, their product / (a) X g (a) is not zero, because its leading term is ...

With these laws of addition and multiplication, the

**polynomials**in x form a ring.The ring has unity: the

**polynomial**of degree zero written 1 . Further, if neither f (x)nor g (x) is zero, their product / (a) X g (a) is not zero, because its leading term is ...

Page 257

Starting from the second equation of (25), the same procedure gives g (x) = e£x)

b£x), in which e£x) is a

g (x), so that f(x) = l (jc) r (x), g{x) = m (jc) r (jc), then t>ix) = \pix) I (x) + qix) m (x)] ...

Starting from the second equation of (25), the same procedure gives g (x) = e£x)

b£x), in which e£x) is a

**polynomial**. If r(x) is a**polynomial**that is a factor of f(x) andg (x), so that f(x) = l (jc) r (x), g{x) = m (jc) r (jc), then t>ix) = \pix) I (x) + qix) m (x)] ...

Page 258

Because F(x^ □ • • , xr) is symmetric, r similar equations result (see 34). Now

consider the

functions ...

Because F(x^ □ • • , xr) is symmetric, r similar equations result (see 34). Now

consider the

**polynomial**H(z), formed by subtracting F(jt|, • • • , xr) from a similar**polynomial**in the variable z (see 35), with coefficients in the field of rationalfunctions ...

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