Review

Exponents and Polynomial Operations

100

2x² + 6x + 5 + 3x² - 2x - 1

1.Like Terms- 5x²+4x+4

2.Answer

200

5y²+2xy-9 - (2y²+2xy-3)

1.Like Terms- 3y²+0-6

2.Answer- 3y²-6

300

(7x⁵y^-3)^-2

1.distibute- 7^-2x^-10y⁶

2.Flip negatives-            y⁶

                                ---------

                                   49x¹⁰

400

5x²y(7x²-4xy²+2y³)

1.Distribute/Answer- 35x⁴y-20x³y³+10x²y⁴

500

(2x² – 5x)(9x² + 6x + 4)

1.Distribute- 18x⁴+12³+8x²-45³-30x²-20x

2.Combine Like Terms- 18x⁴-33x³-22x²-20x

3.Answer- 18x⁴-33x³-22x²-20x

Factoring Polynomials

100

14a⁴+35a²

1.GCF- 7a²

2.Answer- 7a²(2a²+5)

200

x²+8x+15

1.Multiply- x²*15=15x²

2.Split- x²+3x+5x+15

3.Group- (x²+3x) + (5x+15)

4.GCF- x(x+3) + 5(x+3)

5.Answer- (x+5) (x+3)

300

3x²+6x+4x+8

1.Group- (3x²+6x) + (4x+8)

2.GCF- 3x(x+2) + 4(x+2)

3.Answer- (3x+4) (x+2)   

400

2x²+6x³+5x⁷+15x⁸

1.Group- (2x²+6x³) + (5x⁷+15x⁸)

2.GCF- 2x²(1+3x) + 5x⁷(1+3x)

3. Answer- (2x²+5x⁷) (1+3x)

500

2x²+11x+12

1. Multiply-  2x²*12= 24x²

2. Split-  8x*3x=24x²    8x+3x=11x    

3. Group- (2x²+8x) + (3x+12)

4. GCF- 2x(x+4) + 3(x+4)

5.Answer- (x+4) (2x+3)

Radical and Rational Expressions

100

√ 48

1.Simplify- √16*3

2.Split- √16   *   √3

3.Solve- 4√3

200

-2√3 + 3√27

1.Simplify- 3√27= 3√9*3= 3√9  √3=3*3√3=9√3

2.Add- -2√3 + 9√3

3.Answer- 7√3

300

5√15 * 5√20

1.Multiply- 5√15 * 5√20= 25√300

2. Simplify- 25√300=25√100*3

3.Multiply- 25*10*√3= 250√3

4.Answer- 250√3

400

x²-10x-24         5x²-20x

------------  *  --------------

x³+2x²             x²-16x+48

1.Factor/Cancel- (x+2) (x-12)/x²(x+2) * 5x(x-4)/(x-4)(x-12)

2.Multiply/Cancel- (x-12)/x² * 5x/(x-12)= 

5x(x-12)/x²(x-12)

3.Answer- 5/x

500

k⁴-16              4k³+16k

---------   /    --------------

2k²-k-6           12k²+18k

1.Factor/KCF- (k+2)(K-2)(k²+4)/(2k+3)(k-2) *

6k(2k+3)/4k(k²+4)

2.Cancel/Multiply- (k+2)/1 * 6k/4k = 6k(k+2)/4k

3.Cancel/Answer- 6k(k+2)/4k= 3(k+2)/2

Complex Numbers

100

i⁵

1.Multiply- i⁴*i=i

2.Answer= i

200

(8+7i) + (4+3i)

1.Add- (8+4) + (7i+3i)

2.Answer- 12+10i

300

(7+9i) - (3+4i)

1.Distribute- 7+9i-3-4i

2.Like Terms- 7-3+9i-4i

3.Answer- 4+5i

400

(3-2i)(4+5i)

1.3x(4+5)+-2i(4+5i)

2.Multiply/Simplify- 12+15i+-8i 10i² = 12+15i+-8i-10*-1 = 12+15i+-8i+10

3.Adding- 12+10+15i+-8i= 22+7i

4.Answer- 22+7i

500

(3+7i)          (5+2i)

---------  *   ----------

(5-2i)            (5+2i)

1.Multiply- 15+6i+35i+14i²/5²+2²

2.Simplify- 15+6i+35i-14/5²+2²

3.Like terms- 15+6i+35i-14/5²+2² = 1+41i/29

4.Answer- 1+41i/29

Linear Functions

100

2(w+3)−10=6(32−3w)

1.Simplify- 2w−4=192−18w

2.Add- 20w=196

3.Divide/Answer- 49/5

200

4x−7(2−x)=3x+2

1.Distribute- 4x-14+7x=3x+2

2.Like Terms- 11x-14=3x+2

3.Subtract- 8x=16

4.Divide- x=2

5.Answer- x=2

300

2(8+2x)=6x+10

1.Distribute- 16+4x = 6x+10

2. Subtract- -2x+16+10

3.Subtract- -2x=-6

4.Divide- x=3

5.Answer- x=3

400

  4t                1

-------   =   -------

 t²-25           5-t

1.Factor- 4t/(t-5)(t+5)=1/-(t-5)

2.LCD-(t-5)(t+5)

3.Multiply- (t-5)(t+5)*(4t/(t−5)(t+5))=4t 

 -(1/t-5)*(t-5)(t+5)= -(t+5)

4.Distribute- 4t=-t-5

5.Add- 5t=-t

6.Divide/Answer-  t=-1

500

0.02x+0.08(8-x)=1.78

1.Distribute- 0.02x+0.64-0.08x=1.78

2.Like Terms- -0.06x+0.64=1.78

3.Subtract- -0.06x=1.14

4.Divide/Answer- x=-19