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XII. The verifications of the expressions under this number may be readily effected by performing the indicated operations.
XIII. The exercises under this number will occasion no difficulty. The identical expressions may be expanded or resolved into the same factors.
9. The three expressions under this number are each reducible to a® +6° +c6 – 6(a*bc + 64 ac + cab) + 2(a368 +a%c3 +68c8) + 9ab*c*.
XX. 1. It is obvious that bx+cy must be one of the factors, and that x2 +axy + y? must be divisible by bx+cy. After performing the division the remainder will be K1-lab - c)c \ y', which must be equal to zero, in order that the division may na 62 leave no remainder.
2. The coefficient of x4 is 3a4.
3. Four factors of the form x+a and one of the form x – b. See Section IV., Art. 12, pp. 19, 20, and the note.
4. x3 + px? +px+1=(208 +1)+ px(x+1); and 2+1 is always divisible by x+1 when n is an odd number.
5. See Section IV., Art. 13, p. 24.