Factoring r'ractice #1: This is probably one of the most important skills to be proficient at to be successful in PreCalc
IUS!
Use the attached "factoring notes" to brush up on your factoring skills. Factoring is taught in Algebra 1 and Algebra 2. We will not be
spending a lot of class time on factoring. Come get help quickly if you have problems with these! Factor all of these completely.
EXPRESSION
TYPE
16m2n + 12mn2
GCF
1.
FACTORED
Lf YY\n
(
Lf VY\
+ ~n)
2.
x2
-
2x
GCF
X (x-?-)
3.
x2
-
25
Diff. of Perfect Sq' s
(X -\-t5) ('IC -5)
4.
x4 -1
Diff. of Perfect Sq's (twice)
,
'.
5.
3a2
6.
x3 + 125
(+
-
27b2
)C -
Combo: GCF & Per. Sq's
+
FORM
(x'2 + I) (X + l)(X-r)
3(a'l - tf b~ -'7~3(a + 3b) (tt-31?) 1
Sum of Perfect Cubes
eX + 5) [X~-
5)(
-t :LS)
)
+ bLf)
7.
a3 _ b6
Diff. of Perfect Cubes
(£1-kij (a.'2.+ ah"2.
8.
x3 + 27
Sum of Perfect Cubes
()( + 3) CX7.- 3)(+q)
9.
x2 + 8x + 16
Perfect Square Trinomial
()(+ Lf )()( + L1)
10.
3
Lt
2
+ 32t + 128t
Combo: GCF & Trinomial
Diff. of Perfect Cubes
-12wr+9r
12.
4w
13.
8x3
14.
20x2 -60x-35
+l
J:(+-z,~ Hot +- (0 4)
(-I:-t- ~) C+_ W)j
b+
(ab
-e.~ (cflo~+ (Ahc"%- +~4)
~9~W- =3r)
Perfect Sq. Trinomial
(Jw -
Sum of Perfect Cubes
(2'f-
Combo: GCF & Trinomial
5" 4><. -('2.X-7
+ y ) (ttx2- - 2'1..y + yZ
~ (tX+-:fXzx -7)~
15.
200 + 17r - r2
Trinomial
DO NOT SWITCH THE ORDER!
16.
6x2
17. (4x2
+ lOx - 4
Combo: GCF & Trinomial
+ 8f
Combo: GCF & Grouping
4xy - 8y)
(er, + r)(Z5 -r)
')c~x + 5X -2.IZ ~X -1)« + ;LA
(x;-i) (L1'X- 4y)
lfX(X+i) -tJry(X+2-)
(Y-3)(-'l-X)
Factor Practice #2:
2. 81x2-4
1. x2 -16
(X + 4)(X..- f)
(q)( +2YQX-2)
L
5. x2 + 6xy + 9y2
4. a2b2 -25
(g b tS-)[ab-5)
7. a2 +4a+4
Q<+3yXx+3y)
8. /-6y+9
(Cl+-Z-)(tA +2-)
C'l-3)(Y-3)
11. 25 - a2b2
10. 9x2 +12x-4
(5-t (/\b)[s--ab)
14. 64a3 +27
13. x3 -27
(tilt +3)(J~?--12o.+tt)
(y.- 3) (X~+3X +q)
16. 1-125b3
17. x3/+64
(r- 5b)(r + 5b+25k'1-)
@-b)-h) (a.~2l)h+t:
~
62-)
+~b-b + J
(a-2-~(
4;z._~b +loz)
6. 49a2 -16b4
(J1C\ t- Lf b-Z-)(rta -Lfb1--)
9. 1-9a2
(\- 3c9{ (+ 3a)
12. 4a2 - 36ab + 81b2
Cza-qOC'2Q-q~
15
3
~xy
+~
(t}x7..'17-- flXy +tt)
+
3
C;-t~)(~- mY! + ~"2)
18.27x3-8/
'Z.
~)(- 2y)(q~+l4xy+Lfy2)
(XY+4)(x7y:-LfXY+llo)
20. 8x3/ +27
19. (a - b)3 _ b3
••
3. 16x2 -40x+25
21.
2y2 -8.xy+15
X
fty -3Y..'It'f -
5)
2_. alb:! .lOab
(ab
23. H~-13b2 -90
_4
24. a4b4 +11a2b2 -26
(~l--l~~~
-r- 5)
ce oJn-Y )
26. 10a2b2 +3ab-7
25. 3X2y2 -14xy+1S
(3XY - 5~y - ~)
&Oab -7Xab
0-'th~+ IB)@-zb'"
-:2)
27. Sx2 +10x+S
+ I)
+ 2X + I)
l5 eX -\- ,'Xx;- r)]
5{X't-
30. 16x4-81
29. y4-10/+21l
y'2.(y'Z._ rD + Z \)
(4 x'Z- -t-li1){LJ}('Z-- ~)
Y 'l-(y _ 3)(: _ 7 ) [~ x~-t61) ('2 X +"?» ( t )(-3)]
X-
3
3
31. x / _x
3
32. (2x +4x
3X-6)
33.
t
3
+8.~t9x-18)
(f. Y - x) {X"y7.-+ x.7.y -+ x"") ~()( +~-3 ()( t-2-) Lf)f)( + 1j -4 ()( +7.)
lE....f-"2.)[ Z)(~- 3)]
(x n.) ('2)( +3) ('2 )(-3)
4
34. x -2x3-3Sx2
x2 (X"Z- - 2.X-35)
[ x:z:ex - t"/ )D;;! '5
3S.8x4-40x3+S0X2
n
'2X'2- LfX1:..ZDX +2~
Z'f..~ fly. -5[.:z)( - '5
37. a4-2Sa2-144
38. x4y2_SX3/+6x2y4
'l" -t(y.'t_5Xy-t- ~yj
x'l-l& -?Jy1f -2y)
(a.'Z-
40. ~Xb-8*4b+~)
cg X Cb.- 1) - t{ (h -1)
(b-l)( tx. -Lf)
,=4 ((J-I)(Z"l< -ITI
36. 16a4-b4
(lfctz-+ b2X 4o:7--1:::l)
_
4cil. -tb~ (2.£:-l. t bY'llt -b)]
t
39. 24a2b2-14ab3-90b4
;z. 1l-(l'2-a.Z-- 7a b- tf5/tl)
\TIl@'1A. +- 5h)(~a.-q 1,)1