Factor each of the following using integer coefficients:

(a) x2 + 10x + 21 Here, using the notation from Rule 1 in Section 1.3, m = 1, n = 10, and p = 21. For simplicity we limit our search to positive integers such that:

(1) a · b = 1 [I, 1] Henceforth, when a = b = 1, this step will be omitted and only one order will be considered.

(2) c · d = 21 [1, 21; 3, 7; 7, 3; 21, 1]

(3) ad + be = 10. With a = 1 =

b, (c +

d) must equal 10. Since only 3 + 7 and 7 + 3 = 10,

Whenever a · b = 1, the order of factors is unimportant and only one ordering of a given pair will be mentioned.

Transcribed Image Text:

x+10x+21= (x+3)(x+7) or (x+7)(x+3)