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
