Review

Graphs and functions

100

f(x) = x²+3x - 5

g(x) = x-4

find 5f(-3) - g(x)

-x-1

200

f(x) = 5x²-x + 6

g(x) = 7x²

find f(x+h) - g(h)

5x²+10xh-2h²-x-h+6

300

State domain and range of x²+2 

Domain: All real numbers

Range: (2, infinity)

400

State domain and range of |x|+4

Domain: All real numbers

Range: (4, infinity)

500

State domain and range of √x-14

Domain: (14, infinity)

Range: (0, infinity)

Solving factoring

100

(x-4)²-9 = 0

x = 1, x = 7

200

15a²-3a = 3 - 7a

a = (1/3) , (-3/5)

300

49x³ = 100x

x = (-10/7), x = 0, x = (10/7)

400

8x⁴-3 = -10x²

x = (-1/2) , (1/2)

500

26n⁶-39n⁴+13n² = 0

n = -1 , -(√2)/2 , 0, (√2)/2, 1

Exponents

100

(2x²)^-4

1/(16x⁸)

200

(2h³j^-3k⁴) / (3jk)

(2h³k³) / (3j⁴)

300

[(4x⁰)⁴][x²y^-4][x³y³]

(256x⁵)/(y²)

400

(3x³y^-1z^-1) / (x^-4y⁰z⁰)

(3x⁷) / (yz)

500

(2x⁴y^-4z^-3) / (3x²y^-3z⁴)

(2x²) / (3yz⁷)

Dividing/multiplication polynomials

100

(6n²-6n-5)(7n²+6n-5)

42n⁴-6n³-101n²+25

200

divide -5k²+k³+8k+4 by (-1+k)

k²-4k+4+(8 / (-1+k))

300

(50k³+ 10k² -35k - 7) / (5k-4)

10k²+10k+1-(3/ (5k-4))

400

(4x⁴-6x³-12x+12) / (4x-6)

x³-3-(3/(2x-3))

500

(4x⁴+21x³+39x²-13x-84) / (4x+9)

x³+3x²+3x-10 + (6/ (4x+9))

Factoring

100

x³- (8/125)

(x-(2/5))(x²+(2/5)x+(4/25))

200

28gh+16g-63h-36

(7h+4)(4g-9)

300

(x+y)²- (2x-y)²

-3x²+6xy

400

h²-10h+25-k²

(h-5-k)(h-5+k)

500

(a+b)c²-5(a+b)c-24(a+b)

ac²+bc²-5ac-5bc-24a-24b