Page:Elementary algebra (1896).djvu/95

77 Rh And therefore for (1) we may write (5x+ )(x + ). (2) we may write (5x — )(x — ).

And, since 5x3+1 x 2 = 17, we see that

5 x^2 + 17 x + 6 =(5 x + 2)(x + 3). 5 x^2 - 17 x + 6 = (5 x - 2) (x - 3).

In each expression the third term 6 also admits of factors 6 and 1, but this is one of the cases referred to above which the student would reject at once as unsuitable.

Ex. 3. 9x^2 - 48 xy + 64 y^2 = (3x - 8y)(3x - 8y) = (3x-8y)^2.

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

Note. In Chapter xxvi. a method of obtaining the factors of any trinomial in the form ax^2 + bx + c is given.

EXAMPLES X. e.

Resolve into factors :

1. 2x^2 + 3a:+ 1. 2. 3 x^2 + 5 x + 2. 3. 2x^2 +5 x + 2. 4. 3x^2+ 10x + 3. 5. 2x^2 + 9x + 4. 6. 3 x^2+ 8 x + 4. 7. 2x^2 + 11x + 5. 8. 3x^2 + 11x + 6. 9. 5x^2 + 11x + 2. 10. 3x^2 + a: -2. 11. 4x^2 + 11x-3. 12. 3x^2 + 14x - 5. 13. 2 x^2 + 15 x - 8.

14. 2x^2-x-1. 27. 15 x^2 - 77 x + 10. 15. 3 x^2 + 7 x - 6. 28. 12x^2-31x-15. 16. 2 x^2 + x - 28. 29. 24x^2+ 22x-21. 17. 8 x^2 + 13 x - 30. 30. 72x^2-145x + 72. 18. 6 x^2 + 7 x - 3. 31. 24x^2-29xy-4y^2. 19. 2 x^2 - x - 15. 32. 2 - 3 x - 2 x^2. 20. 3x^2 + 19x-14. 33. 6 + 5 x - 6 x^2. 21. 6x^2-31x + 35. 34. 4 - 5 x - 6 x^2. 22. 4 x^2 + x - 14. 35. 5 + 32 x - 21 x^2. 23. 3x^2-13x + 14. 36. 18-33x+5x^2. 24. 4x^2 + 23x + 15. 37. 8 + 6x-5x^2. , 25. 2 x^2 - 5 xy - 3 y^2. 38. 20- 9x-20x^2. 26. 8 x^2 - 38 x + 35. 39. 10 - 5 x - 15 x^2.

97. We add an exercise containing miscellaneous examples on the preceding cases.

EXAMPLES X. f.

Resolve into factors :

1. x^2 + 13 x + 42. 3. 2x^2 + 7a + 6. 2. 143 - 24 ax + a^2x^2. 4. a^2b^2 -3abc - 10 c^2