1. 5x4
– 405
= 5(x4
– 81)
= 5(x2
+ 9)(x2
– 9)
= 5(x2
+ 9)(x + 3)(x – 3)
by D. Fisherby D. Fisher

3. x2
+ 10x + 16
= (x + 8)(x + 2)

4. x2
+ 4x – 21
= (x + 7)(x – 3)

5. 2x2
+ 7x + 3
= (2x + 1)(x + 3)

7. 3x2
y + 12xy
= 3xy(x + 4)

8. x3
+ 5x2
– x
= x(x2
+ 5x – 1)

10. x2
– 81
= (x + 9)(x– 9)

11. 4x2
– 121
=
(2x + 11)(2x– 11)

13. x2
– 14x + 49
= (x – 7)2

14. x2
+ 8x + 16
= (x + 4)2

15. 25x2
– 10x + 1
= (5x – 1)2

17. x2
– x – 6
= (x – 3)(x + 2)

18. 3x2
+24x + 21
= 3(x + 1)(x + 7)
= 3(x2
+ 8x + 7)

19. x4
– 16
(x2
+ 4)(x – 2)(x + 2)
= (x2
+ 4)(x2
– 4)

20. x2
y +4xy + 4y
= y(x + 2)2

21. 9x2
+ 6x + 1
= (3x + 1)2

22. 2x2
– 18x + 40
= 2(x – 4)(x – 5)