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Kuta Software - Infinite Algebra 2 Name_______________________________________
Rational Expressions Date_______________ Period____
State the excluded values for each.
I) 60x3 2) 70v212x 100v
3) ,n+7 n2+6n+5nr + 4i,z —21 ii + 1
5) 35x—35 6) —n2+16n--6325x—40 n—2n—35
Simplify each and state the excluded values.
) 7p+4 8) ISa—IS
9) 2a+lOa 10) p2—3p—1O3cr+15a p+p—2.
11) x2+x—6 12) a2+Sa+4.r+8x+15 cr+9a+20
x2—2x—1S 10x—613) x2—6x+5 14) 10x—6
15) (v—7)(v+8) 1 16) ÷ (,~— 1)(n+3)(v+8)(v—10) v—10 n+2 (j~1)2
17) x+3 3(x—6) x—8 4x(x+10)18)4 3(x+3) (x+6)(x—8) x+1O
19) 2b2—l2bb---6 20) 1 ÷ 6—tib+5 b+5 ,i+9 3n—18
21) 28—7b 1 22) 2 v2—12v+27b—4 b+1O v2—12v+27 3
23) 1 8—7x—x2 x+524)~ 5p3—35p2 x+8 9x—9
25) x2—16 x2+x—90 26) 10x2—20x 16x3+80x29—x r+14x+40 40x3—80x2 6x+30
Kuta Software - Infinite Algebra 2 Name
Rational Expressions Date_______________ Period____
State the excluded values for each.
1) 60x3 2) 70v12x lOOv
3) m+7 4) n2+6n+5nr+4m—21 n+1
5) 35x—35 6) n2-i-16n—6325x—40 n2—2n—35
{1Simplify each and state the excluded values.
) p+4 8)p +6p+8 iSa—iS
1 3{1}p+2 s(a i)
9) 2a +iOa 10) p23p 103a2 iSa p2+p—2
2;{0, 5 p ~;{2, }
11) x2+x—6 12) a +Sa+4x2+8x+15 a2+9a+20
x—2 ~ ~+5
13) X2 2x—15 14) lOx—6r—6x+5 lOx 6
i, P15
(v—7Xv+8) 1 n+3 (n—l)(n+3)(v+8)(v—1O) v—10 n+2 (fli)2
fl 1;{ 21 3}ii + 2
x+3 3(x 6) x—8 4x(x+1O)4 3(x+3) (x+6)(x—8) x+lO
4x 68 10x+6
19) 2b2—l2bb—6 20) 1 ÷ 6—nb+5 b+5 n+9 3n—18
2h, 5,6 ;{ 9 6}ii + 9
21)28 7b 1 22) 2 v2—12v+27b 4 b+1O v2—12v+27 3
4 iO} 2.{39b+10 3
23) _!__÷ 9’~36 24) 8—7x—x2 x+55p2 5p3—35p2 x+8 9x—9
{o (x9(p 4)’ 9
25) x2—16 x2+x—90 26) 10x2—20x 16x3+80x29—x x2+14x+40 40x3 BOx2 6x+30
(x 4);{9 4 io} ;;{o 2 s}
Kuta Software - Infinite Algebra 1 Name_______________________________________
Adding + Subtracting Rational Expressions Date_____________ Period___
Simplify each expression.
u+Sv u—6v Sn 2m+4n1) 2) +8vtr 8vtr 30m 3Oin
3) a+2b — Sa+4b 4) x+y — 6x+y6a3 6a3 i8xy i8xy
4a—5 a—i 5x—4 — x+65) 6a2 + 30a + + 6) 9x3 + 27x2 9x3 + 27x2
b—3 4b n—4 n+i7) + 8),i2b+i8 12b+18 tr—n—20 n—n—20
7x x—2 8 49)—— 10)2x 20x+i6 7v—6 3r
ii) 7v 8v—4 12) — ___
8 Sv—2 n+7 ;i—2
7 7 6 713) 3n2+24n — 14) v—2 — 2v+7
6x 7 5v S16) +
3 lSx+3 v—3 v+6
4x 5 2 6x17) x2+4x—5 —— 18) x+3 — 2x+1
19) 4x — 4x 20) 2x — 2x+3 x+6 3x+3 x+5
21) 6 + 6 22) v—2 +3vx—2 x+1 3v4—15v3—18v2
Kuta Software Infinite Algebra 1 Name
Adding + Subtracting Rational Expressions Date_____________ Period___
Simplify each expression.
u+Sv u—6v Sn 2m+4n1) — 2)—+
8v2u2 8v2u2 30m 30m
9n 2mOni
3) a+2b — Sa+4b 4) — 6x+y6a3 6a3 iSxy l8xy
—2a b30
4a—5 a—i Sx—4 — x+65) 6a2-t-30a ~6a2+3oa 6) 9x3+27x2 9x3+27x2
So 6 4x—1O6a +30a 9x +27x
b—3 4b n—4 n+i7) + 8)212b+i8 12b÷18 n —n—20 n —n—20
Sb 3 212 3l2h+18 n 20
7x x—2 8 49) — 10)2x 20x+i6 7v—6 3v2
69x 58 24v2+28v 244(5 i + 4) 3v2(7v 6)
11) 7v 8v—4 12)8 Sv—2 ii 7 n—2
35v 78v+32 3,1—578(Sv 2) (n + 7)(n 2)
13) 14) 6 73n2+24n 2n v—2 2v+7
154 2112 Sv+566,i(iz + 8) (2v + 7)(v 2)
6x 7 Sv 515) + 16) +3 15x+3 v 3 v+6
30x +6x+7 S +35v 153(Sx+ (v+6)(v 3)
17) 4x 18) 2 — 6xx2+4x—5 4 x+3 2x+1
4x 5x +25 4x+2 6x4(x+5)(x 1) (2x+1)(x+3)
19) 4x — 4x 20) 2x — 2x+3 x+6 3x+3 x+5
2x 2.~ +4x 6(x+3)(x+6) 3(t+1)(t-i-5)
6 6 v—221) + 22) +3vx—2 x+1 3v4—15v3—18v2
12x 6 9v 45v4—54v3-i-v—2(x+ 1)(x 2) 3v (v+ 1)(v—6)
Kuta Software - Infinite Algebra 2 Name___________________________________
Adding/Subtracting Rational Expressions Date__________ Period
Simplify each expression.
it—i’ 6u—3v m—3n tn+3n1) + 2) — _____
8v 8v 6m3n 6m3n
S 5a+1 53), + 4) , + 7a+3a+2 a2+3a+2 lO,r+16n+6 10n+16n+6
r+6 r+l x+2 x+35) + 6)
3r—6 3r—6 2x2+l3x+20 2r+13x+20
7) 6 —~ 8)6— x+Sx—1 4 (7x—S)(x+4)
3 4 3 79) + 10) ., ——
x+7 x—8 4ir+4v 2
7 8 5 41211)—— 12) +3 12x—8 ,i+S 2n+6
2x 6x 2 813) + 14) 2Sx+4 2x+3 3x +12x 2x
7n 8 2 415) + 16) +,z+1 iz—7 n+8 n+1
3 3 3 717)—— 18) +8 3x+4 b—8 b+3
3 7 4 219) + 20) — ____
x+6 x—2 x+1 x+2
Sn+5 7n 3 621) +— 22) +5n2+35n—40 3,7 n—5 3,z—8
25 24) 84 4 1623)
1 4 995 25
a a 525)255 26)
a 5 4in in
Critical thinking questions:
a c 28) Split into a sum of two rational expressions27) Simplify: — + — with unlike denominators:b d
2x +3+ 3x +2
Kuta Software - Infinite Algebra 2 Name
Adding/Subtracting Rational Expressions Date_____________ Period___
Simplify each expression.
u—v 6u—3v m—3n m+3n1) + 2) — 38v 8v 6m3n 6ni n
7,, 4v8v
S Sa+1 S n—6___3) + 4)a2+3a+2 a2+3a+2 10n2+16n+6 10n2+16n+6
6 5c 1+na +3c+2 iOn +16n+6
r+6 r+i x+2 x+35) + 6)
3r—6 3r—6 2x2+13x+20 2x +13x+20
2r+73r 6 2x2+ 3x+2
7) 6 8)6— x+Sx—1 (7x—5)(x+4)
24 5x2 Sx 42x2+ 37x—1254(x i) (7x 5)(x+4)
9) + 10) 2 ——
x+7 x—8 4v +4v
7x+4 3 14v 14v(x+7)(x 8) 4v(v+
7 8 5 4nii) 12) +3 12x—8 n+5 2n+6
21x 20 5n+ 5+2,i3(3x 2) (‘~ + 3)(n + s)2x 6x 2 813) + 14)
Sx+4 2x 3 3x2+12x 2x
3 +30x 50+12x(5x + 4)(2x + 3) 3x(A + 4)
7n 8 2 415) + 16) +n+1 ii 7 n 8 n+1
7n 41n+8 6,z+34+ 1)(n 7) (n + i)(n 8)
17)~— ~ 18) +8 3x+4 b—8 b+3
9t 2 Ob 478(3x + 4) (b + 3)0 8
19) + 20) — 2x+6 x—2 x+1 x+2
lOx+36 2x+6(x+6)(x 2) (x+1)(x+2)
Sn+5 7n 3 621) 22) +5n2+35n—40 3n n—S 3n—8
52n 53 7n lSn 543(n + 8)0 i) (3rz 8)(n 5)
25 24) 84 4 1623)
1 4 995 25
a a S
25) 25 ~ 26)a 5 4
m m
Critical thinking questions:
a c 28) Split into a sum of two rational expressions27) Simplify: -~ + with unlike denominators:2x + 3
ad+bc 2x +3x+2bd
Man olutions Ex:x+1 x+2
Kuta Software - Infinite Algebra 2 Name_______________________________________
More on Factors, Zeros, and Dividing Date_____________ Period___
Factor each ~&fiad-aflze~os,- One factor has been given.
1)f(x)=x3+9x2+23x+15;x+5 2)f(x)=x3—x2—14x+24;x—3
3) f(x)=x4+3x3—13x2—lSx; x—3 4) f(x)=x3—12x2+47x—60; x—3
5) f(x)=x3 —7x2 +2x+40; x—5 6) f(x)=x3 —3x2 —9x+27; x—3
7)f(x)=10x3+37x2+37x+6; 5x+1 8)f(x)=25x3+150x2+131x+30; 5x+3
9) f(x)=5x3+21x2—21x--5; x+5
11) f(x)=51+9x2—26x—24; x+3
Factor each
13) f(x)=5x3+
10) f(x)=3x3—4x2—9x+10; x—2
12) f(x)=6x3+7x2—1; 2x+1
~19x2~2x -~
all zeros. One zero has been given.
2 14) f(x)=25x4
15) f(x)=3x4+5x3-i-81x+135; —~16) f(x)=2x4—x3—18x2+9x —3
+32x+20;!2
18) f(x)=3x3 —35x—12; 317) f(x)= 101
Kuta Software - Infinite Algebra 2 Name
More on Factors, Zeros, and Dividing Date______________ Period____
Factor each aml-fhid-aII-zeros1- One factor has been given.
l)f(x)=x3+9x2-i-23x+15;x-i-5 2)f(x)=x3—x2—14x-i-24;x—3
Factor to: f(x) — (.~ + I )(x + + s) Picto s to. f(x) )(x + 4)(x 3)
3) f(x)=x4+3x3—13x2—15x; x—3 4) f(x)=x3—12x2+47x—60; x—3
Factor to f(x x(x l)(x+ 5)(x 3) Factors to: f(x) = (x 4)(x 5)(x 3)
5) f(x)=x3—7x2+2x-i-40; x—5 6) f(x)=x3—3x2—9x+27; x—3
Factors o f(x) (x + 2)(x 4)(x s) Factors to f(x) (x + 3)(x — 3)2
7)f(x)=10x3+37x2+37x-i-6; 5x+1 8)f(x)=25x3+150x2+131x-i-30; Sx+3
Factors to f(x) = (2x + 3)(x + 2)(5x + i) acto s to: f(x) — (Sx + 2)(x + 5)(Sx + 3)3 1 2 32 5 5’ ‘5
9) f(x)=5x3+21x2—21x--5; x+5
actors to: f(x) = (5x + 1)(A — 1)(x + 5)1S
10) f(x)=3x3—4x2—9x+1O; x—2
Factors o f(x) — (3x + 5)(x53
i)(x 2)
Factor each and find all
13) f(x)=5x3+4x2 20x
15) f(x) = 3x4 +5x3 + 81x+ 135;
17) f(x)=10x3—41x2+32x+
Facto s 0: f(x) (Sx +12 5Zeros: , 2,15 2
i)(x 3)(x+3)
+ )(x+4)(r 3)
11) f(x)=5x3+9x2—26x—24; x+3
Factors to: f(x) — (5x + 4)(x 2)(x + 3)4 15’ ‘ 3’ ‘ 2
One zero has been given.
12) f(x)=6x3+7x2—1; 2x+1
Factors to: f(~)—(3~ iXx+ 1)(2x+ i)
19x2—2x; ~5
x(5r+1) (Facto s to: f(x) = (5x + 4)(x
14Zeosi ,2215
2)14) f(x)=25x4—
Factors to f
mult.2,25
— — 18x2 + 9x; —3
Factors to f(x) — x(2x1, ~2
Facos o:f(x)=(x+
Zeros { ~ 3 + 3i~2
‘~( 73)~r 3x3
+ 9)(3x +5
2 3
Zeros: 0
S2
18)
(~ 2)(2x S
4x2—35x—12; 3
Factors to:
Zeros: {3
Kuta Software - Infinite Algebra 2 Name_______________________________________
Factoring Quadratic Form Date______________ Period___
Factor each completely.
1) u4+2u2 2) x4+x2—12
3) a4+6a2+S 4) x4—8x2+15
5) u4~4u2 —5 6) ,n4+9m2+20
7) x4+4x2+3 8) x4—7x2+1O
9) 74 — 54,~2 — 16 10) 7u4 + 41u2 + 30
11) 5x4—9x2+4 12) 3x5—2x3—8x
13) 2x6+13x4+6x2 14) 2a4—6a2+9
15) 7m4—44m2+12 16) 3u4—u2—14
17) x6—9x3+8 18) 6x9n—30x5n—300xn
19) x6+4x3—60 20) 5nu8—15nu4+40n
21) x6+2x3—3 22) m6—81
23) —x6+2?+15 24) x7m+2x4m—lSxm
Critical thinking questions:
25) Whyisthisnotinquadraticform? 26) Factor x2”+9x”—10+ 5x’ +6
Kuta Software - Infinite Algebra 2 Name_______________________________________
Factoring Quadratic Form Date______________ Period___
Factor each completely.
1) u4+2u 2) x4+x2—12
u (, + 2) 3)(.x + 4)
3) a4+6a2+5 4) x4—8x2+15
)(a +s) (1 3)(x2 s)
5) u4—4u2—5 6) m4+9m2+20
5)(u + i) (in + 4)(rn + s)
7)x4+4x2+3 8)x4—7x2+1O(x2+3)(x2+ ) Cr 2)(x s)
9) 7m4—54m2—16 10) 7u4+41u2+30
(7m + 2X,n 6)(u2 + 5)
11) 5x4—9x2+4 12) 3x5—2x3—8x
(5x 4Xx+ i)(v .x(3x +4)(x2 2)
13) 2x6+13x4+6x2 14) 2a4 6a2+9
x (2A + OCt + 6) Not actorable
15) 7m4—44rn2+12 16) 3u4—u2—14
iO,2 + 2)
17) x6—9x3+8 18) 6x9n—30x5n—300xn
Ct 2)(x2 + 2x + 4)(x 1)(x x i) 6xn(x4 io)(t4 5)
19) x6+4x3—60 20) Snu8—15nu4-t-40n
(x 6)(x~
21) x6+2x3—3 22) m6 81
)(x + x + 1)(x 3) (in + 9)(m
23) —x6 + 2x3 + 15 24) x7m + 2x4m — lSxm
(x3 s)( + 3) xrn(x 3)(x + s)
Critical thinking questions:
25) Why is this not in quadratic form? 26) Factor: x2” + 9x” — 10x6+5x4+6 (~ +
The mkl le term shou d have not
Kuta Software - Infinite Algebra 2 Name___________________________________
Factoring: All Techniques Combined (Hard) Date_________ Period
Factor each.
1)x3—5x2—x+5 2)x4—2x2—15
3) x6—26x3—27 4) x6+2x4—16x2—32
5) x4—13x2+40 6) x9—x6—x3+l
7) x6—4x2 8) x4+14x2+45
9) 2x4+x2—6 10) 2x2—13x+20
11)4x3—x2—4x+1 12)4x8—61x4+225
13) 5x2+24x—5 14) 5x2+29x+20
15) 4x2+4x—15 16) 10x3—8x2+25x—20
17)27x9+x6—27x3—1 18)8x4+10x2—3
Kuta Software - Infinite Algebra 2 Name___________________________________
Factoring: All Techniques Combined (Hard) Date_____________ Period
Factor each.
1)x3—5x2—x-i-S 2)x4—2x2—15
(x 5)(r+1)(x i) (~ 5)(x +3
3)x6—26x3—27 4)x6+2x4—16x2—32
(~ 3)(x2 + it + 9)(x + 1)(x x + i) (x2 2)(x + 4)(x + 2)(x 2)
5)x4—13x2+40 6)x9—x6—x3+1
(x 5)(x 8) (x 1)(x +x+1)2(x+1)(x —x+1)
7) x6—4x2 8) x4+14x2+45
x(x 2)(x +2) (~ +5)(x 9)
9) 2x4+x2—6 10) 2x2—13x+20
(2x2 — 3)(x2 + 2) (2x 5)(x 4)
11)4x3—x2—4x-i-1 12)4x8—61x4+225
)(x+ i)(r (it + 5)(2x 5)(x + 3)(x 3)
13) 5x2+24x—5 14) 5x2+29x+20
(Si 1)(x+S) (5x+4)(x+5)
15) 4x2+4x—15 16) 10x3—8x2+25x—20
(2x 3)(2x + 5) (Si 4)(2x + 5)
17) 27x9+x6—27x3 —1 18) 8x4+ lOx2 —3 (2x+ )(2x— 1)(2x2 +3)
(3A+1)(9x 3c+ )(x i)(r x+ )(x 1)(x +i+i)
