Semester 1 Review

Factor A

100

X²-16

(x-4)(x+4)

200

-2x⁴+4x²

-2x²(x²-2)

300

9y⁴-25

(3y²-5)(3y²+5)

400

8x²+6x

2x(4x+3)

500

-2x²=8x

-2x²-8x=0

-2x(x+4)=0

-2x=0  x=0

x+4=0  x=-4

Factor B

100

6x²+11x-10

(3x-2)(2x+5)

200

x²-3x-10

(x-5)(x+2)

300

x⁴-18x²+81

(x²-9)(x²-9)

(x-3)(x+3)(x-3)(x+3)

400

8x²-60x+28

4(2x²-15x+7)

4(2x-1)(x-7)

500

x²-3x=10

x²-3x-10=0

(x-5)(x+2)=0

x-5=0  x=5

x+2=0  x=-2

Solve A

100

6x³+3x²+8x+4

3x²(2x+1)+4(2x+1)

(2x+1)(3x²+4)

200

3x³-3x²-4x+4

3x²(x-1)-4(x-1)

(x-1)(3x²-4)

300

8x²-60x+28=0

4(2x-1)(x-7)=0

2x-1=0  x=1/2

x-7=0  x=7

400

x³-3x²-4x+12

x²(x-3)-4(x-3)

(x-3)(x²-4)

(x-3)(x-2)(x+2)

500

3x³-2x²-6x+4

x²(3x-2)-2(3x-2)

(3x-2)(x²-2)

Solve B

100

(2x-3)²=5

2x-3=+/- root 5

x= 3 +/- root 5 over 2

200

3x^3/2-81=0

3x^3/2=81

x^3/2=27

x³=27³

x³=729

x=³root729  x=9

300

4 lx-5l -16=0

lx-5l = 4

x-5 = 4  x=9

x-5 = -4  x=1

400

(3x-2)²=12

3x-2= +/- root 12

3x= +/- root 12 +2

x= +/- 2 root 3 +2 over 3

500

5x^3/2-40=0

5x^3/2=40

x^3/2=8

x³=8²

x³=64

x= ³ root of 64 = 4

Misc

100

4x²-9

(2x-3)(2x+3)

200

x⁴-18x²+81

(x²-9)(x²-9)

(x-3)²(x+3)²

300

x²-2x=15

x²-2x-15=0

(x-5)(x+3)=0

x=5, -3

400

9x²-9x+2=0

(3x-2)(3x-1)

3x-2=0  x=2/3

3x-1=0  x=1/3

500

3x²=6x

3x²-6x=0

3x(x-2)

x=0, 2