Page:Elementary algebra (1896).djvu/88

70 Rh CHAPTER X.

Resolution into Factors.

86. Definition. When an algebraic expression is the product of two or more expressions, each of these latter quantities is called a factor of it, and the determination of these quantities is called the resolution of the expression into its factors.

87. Rational expressions do not contain square or other roots (Art. 14) in any term.

88. Integral expressions do not contain a letter in the denominator of any term. Thus, x^2 + 3xy + 2 y^2, and {1}{3}x^2 + {1}{2} xy —  {1}{2} y^2 are integral expressions.

89. In this chapter we shall explain the principal rules by which the resolution of rational and integral expressions into their component factors, which are rational and integral expressions, may be effected.

WHEN EACH OF THE TERMS IS DIVISIBLE BY A COMMON FACTOR.

90. The expression may be simplified by dividing each term separately by this factor, and enclosing the quotient within brackets; the common factor being placed outside as a coefficient.

Ex. 1. The terms of the expression 3 a^2 — 6ab have a common factor 3a.

3a^2-6ab = 3a(a-2b).

Ex. 2. 5 a^2bx^3 - 15 abx^2 - 20 b^3x^3 = 5 bx^2(a^2x - 3 a - 4b^2).