Part 8

x^2 + x - 30 = (x + 6)(x - 5).

CASE V. A trinomial of the form ax^2 + bx + c. Three terms.

20x^2 + 7x - 6 = (4x + 3)(5x - 2).

CASE VI.

A. The sum or difference of two cubes. Two terms.

x^3 + y^3 = (x + y)(x^2 - xy + y^2); x^3 - y^3 = (x - y)(x^2 + xy + y^2).

B. The sum or difference of two like powers. Two terms.

x^4 - y^4 = (x - y)(x^3 + x^2y + xy^2 + y^3); x^5 + y^5 = (x + y)(x^4 - x^3y + x^2 y^2 - xy^3 + y^4).

CASE VII. A common polynomial factor. Any composite number of terms.

t^2 p + t^2 q - t^2 r - g^2 p - g^2 q + g^2 r = t^2 (p + q - r) - g^2 (p + q -r) = (p + q - r)(t^2 - g^2) = (p + q - r)(t + g)(t - g).

CASE VIII. The Factor Theorem. Any number of terms.

x^3 + 17x - 18 = (x - 1)(x^2 + x + 18).

FACTORING

Review the Cases in Factoring (see Outline on preceding pages) and write out the prime factors of the following:

1. 8a^(13) + am^(12).

2. x^7 + y^7.

3. 4x^2 + 11x - 3.

4. m^2 + n^2 - (1 + 2mn).

5. -x^2 + 2x - 1 + x^4.

6. x^(16) - y^(16). (Five factors.)

7. (x + 1)^2 - 5x - 29.

8. x^4 + x^2 y^2 + y^4.

9. x^4 - 11x^2 + 1.

10. x^(2m) + 2 + 1/(x^(2m)).

11. x^(6m) + 13x^(3m) + 12.

12. 4a^2 b^2 - (a^2 + b^2 - c^2)^2.

13. (x^2 - x - 6)(x^2 - x - 20).

14. a^4 - 8a - a^3 + 8.