Page:Elementary algebra (1896).djvu/124

106 Rh 4. Find the highest common factor and the lowest common multiple of x^3 + 2 x^2 - 3 x, 2x^3 + 5x^2 -3x.

5. Find the lowest common multiple of 1-x, (1 - x^2)^2, (1 + x)^3.

6. Find the lowest common multiple of x^2 - 10x + 24, x^2 - 8x + 12, x^2-6x+ 8.

7. Find the highest common factor and the lowest common multiple of 6x^3 + x^2 - 5x - 2, 6x^3 + 5x^2 - 3x - 2,

8. Find the lowest common multiple of (bc^2 - abc)^2, b^2(ac^2 - a^3), a^2c^2 + 2ac^3+ c^4.

9. Find the lowest common multiple of x^3 - y^3, x^3y - y^4, y^2(x - y)^2, x^2 + xy + y^2. Also find the highest common factor of the first three expressions.

10. Find the highest common factor of 6x^2- 13x + 6, 2x^2+ 5x- 12, 6x^2 -x- 12. Also show that the lowest common multiple is the product of the three quantities divided by the square of the highest common factor.

11. Find the lowest common multiple of x^4 + ax^3 + a^3x + a4, x^4 + a^2x^2 + a^4

12. Find the highest common factor and the lowest common multiple of 3 x^3 - 7 x^2y + 5 xy^2 - y^2, x^2y + 3 xy^2 - 3 x^3 - y^3, 3 x^3 + 5 x^2y + xy^2 - y^3.

13. Find the highest common factor of 4x^3- 10x^2 + 4x + 2, 3x^4-2x^3-3x + 2.

14. Find the lowest common multiple of a^2 - b^2, a^3- b^3, a^3 - a^2b, -ab^2 - 2 b^3.

15. Find, the highest common factor and the lowest common multiple of (2 x^2- 3 a^2)y + (2 a^2 - 3 y^2)x, (2 a^2 + 3 y^2)x + (2 x^2 + 3 a^2)y.

16. Find the highest common factor and the lowest common multiple of x^3 - 9x^2 + 26x - 24, x^3 - 12 x^2 + 47 x - 60. 17. Find the highest common factor of x^3 - 15 ax^2 + 48 a^2x + 64 a^3, x^2 - 10 ax + 16 a^2.

18. Find the lowest common multiple of 21 x(xy - y^2)^2, 35 (x^4y^2 - x^2y^4)y, 15 y(x^2 + xy)^2.